Starch is the second most abundantly available natural polymer in the world, after cellulose. If we add its biodegradability and non-toxicity to the natural environment, it becomes a raw material very attractive for the food and non-food industries. However, in the latter case, mainly due to the high hydrophilicity of starch, it is necessary to carry out many more or less complex operations and processes. One of the fastest growing industries in the last decade is the processing of biodegradable materials for packaging purposes. This is mainly due to awareness of producers and consumers about the dangers of unlimited production and the use of non-degradable petroleum polymers. Therefore, in the present review, an attempt was made to show the possibilities and limitations of using starch as a packaging material. The most important physicochemical features of this biopolymer are discussed, and special attention is paid to more or less environmentally friendly methods of improving its processing properties. Humanity increasingly understands that the earth is not an unlimited source of raw materials and that the overexploitation of natural resources causes a lot of damage to the environment. Everyone can agree that the world economy should be increasingly based on renewable raw materials and energy sources. The growing demand for new organic materials and energy demand encourages the search for cheap, widely available biodegradable raw materials and environmentally friendly methods of their processing . It seemN,N-dimethylacetamide/lithium chloride (DMAc/LiCl), or pyridine. Mainly their flammability and high toxicity are the features that pose a serious threat during the washing and recovery process and thus can be a considerable and troublesome pollution for the natural environment BF4), and others have proved to be effective starch solvents. Ionic liquids, as well as other solvents, are used in starch modifications in order to loosen its macrostructure by breaking inter- and intra-molecular bonds, thereby increasing its reactivity [An interesting idea was to carry out esterification or etherification in ionic liquids (ILs). These are compounds with ionic structures, more specifically consisting of an organic cation and an organic or inorganic anion. Despite this structure, they are not typical salts, because their melting point is lower than 100 °C. Their unusual properties and considerable design possibilities through structural modifications give them a considerable advantage in competing with classic organic solvents. They are non-volatile compounds with high durability and thermal inertness, characterized by high polarity, electrical conductivity, and a wide range of electrochemical stability. Multifunctionality is also a feature of ILs that distinguishes them from other solvents ,139,140.activity . In ordeactivity ,8. In adactivity ,145,146.2 (scCO2) is a non-polar, non-toxic, and chemically inert solvent and easy to remove from the reaction system by expansion. In particular, CO2 in the supercritical state is capable of lowering the starch gelatinization temperature through diffusion into its interior and deformation of crystalline areas. The scCO2 as the solvent was used for the first time in the transesterification of potato starch with vinyl or methyl esters of fatty acids in the presence of basic salts, as well as esterification with anhydrides . Chi et al. conducted an alkaline catalyzed reaction of pre-emulsified DDSA anhydride with granular starch . In anotStarch esters and other hydrophobic starch derivatives synthesized in various ways were primarily used in the production of various types of mixtures with synthetic polymers. For example, the blends obtained by the process of reactive extrusion of acetylated and oxidized banana starch with LDPE. Owing to the use of reactive extrusion, mixtures were also made of thermoplastic corn-starch maleate with poly  (PBAT) and acetylated cassava starch with an aliphatic polyester–polyurethane . The proFor decades, plastics have been considered a boon to the modern world. Only recently, among the society as a consumer, awareness arose about the threat and problem of their high resistance to degradation. The environmental impact of sustainable plastic waste is a matter of general concern around the world, and disposal methods for waste are still insufficient. Space for landfills are limited, combustion utilization can generate toxic air pollutants, and mixed-waste recycling methods are often energy consuming and therefore not cost effective . In addi2 and CO2. The direct use of native starch or even thermoplastic starch as raw materials for packaging production is limited by their fragility, lack of compatibility with hydrophobic polymers, high moisture sensitivity, and poor water-vapor barrier, as well as low resistance to mechanical factors such as tearing and picking [Among biodegradable polymer materials for packaging, starch is the most popular, just after cellulose . This po picking . Starch  picking .Starch-based packaging is made in most cases from corn and potato starch, which may not be surprising due to their significant resources around the world. The use of high amylose corn starch as a packaging material compared to normal starch enabled the development and obtaining of films with higher barrier and mechanical strength. One of the oldest and generally the most commonly used methods to date of using starch as a packaging material is blending it with other natural or synthetic polymers , Table 7Blending TPS with polyesters or other plastics in the vast majority of cases improves mechanical properties and hydrophobicity, as well as resistance to biotic and abiotic factors. Due to the fact that we can isolate starch from many botanical sources, obtaining thermoplastic starch is a relatively inexpensive way of producing biodegradable and renewable products. Another advantage of TPS is that it can be obtained with the same techniques as commercial plastics , which can be an alternative to the use of resistant or poorly degradable plastics, especially in applications with a short life ,47. Howeco-3-hydroxyoctanoate) (PHBO), poly  (PHBV), PHEE, and poly (succinate-co-adipate butylene) (PBSA) [The joining of polymers to produce packaging material can take place not only by mixing but also by forming layers, i.e., layering. In recent decades, coextrusion has been widely used to combine two or more polymers into multilayer coatings. Multilayer products composed of TPS and polyesters can also be produced in the coating and press molding processes. Scientific and industrial research on thermoplastic starch mainly concerned mixing plasticized starch with hydrophobic biodegradable polyesters with much better mechanical properties, type PLA, PCL, poly (ethylene adipate) (PEA), poly (3-hydroxybutyrate-) (PBSA) ,195,196.) (PBSA) . The res) (PBSA) . The mos) (PBSA) . For exa) (PBSA) . In anot) (PBSA) . In thesAlready many years ago, a partially biodegradable blend of starch with LDPE was developed, which in time was particularly useful in the production of food packaging . From thMatzinos et al. using conventional extrusion, injection molding, and film blowing techniques, also processed ternary blends of LDPE/TPS/PCL. The test results confirmed that the structure and properties of the mix depend not only on the composition but also on the processing method. In the films, the fine dispersion of the polycaprolactone phase in the polyethylene/starch matrix caused an increase in mechanical properties . Using tGenerally, to convert native starch or a derivative thereof into a thermoplastic form, it is sufficient to use a hydrophilic biodegradable polymer such as an aliphatic polyester, polyester amide or urethane, polyethylene oxide, or mixtures thereof.Starch films with increased moisture resistance can also be obtained by preparing multilayer sandwich-type structures with a central thermoplastic starch layer and hydrophobic components on the outer layers . However2O soluble polymers for production, which is poly . The materials thus obtained were characterized by high flexibility and strength, which was the result of relatively good mechanical compatibility with a rather low degree of miscibility and formation of so-called continuous polymer phase [In order to maintain biodegradability of mixtures with thermoplastic starch, a number of types of blends with other natural polymers such as pectins or more often biodegradable polyesters such as PHBV, PCL, PLA, PEAs, or PBSA were carried out. The obtained blends were characterized by improved mechanical properties, increased hydrophobicity, and water-vapor impermeability. Their disadvantage was still poor compatibility and poor surface properties . Hence, er phase . The mecAttempts have also been made to produce packaging materials based on hybrid starches, i.e., mixed starches from various botanical sources. Therefore, the focus was mainly on starches with an increased content of amylose, i.e., corn and rice starch, to create a hybrid polymer material, with increased mechanical resistance and improved processing properties .®, in turn, improves the mechanical and functional properties of packaging based on starch and PVOH, which due to their high compatibility and biodegradability can compete with packaging obtained from petroleum polymers [Extrusion of nanocomposite films is another approach in the manufacture of starch packaging materials. Nanocomposites refer to materials with a heterogeneous structure, whose individual components do not dissolve in relation to each other and show different properties. Most often, nanocomposites in starch-based packaging are in the form of nanofiller. They are introduced into the system not only to improve mechanical strength and increase the barrier to gases and steam but also to reduce production costs by reducing the consumption of the more expensive main component. Nanocomposites based on starch and clay are already known, serving as a starting material for the development of biodegradable packaging films . Nanoclapolymers . Films bpolymers .Another example was starch grafted on vinyl emulsion, which was biodegradable and can be used as a sustainable packaging material . BiodegrIn turn, Fang et al. focused on the use of modified starch film (acylated potato starch) as a laminate component in combination with other polymers such as PLA in one of their papers . Based oThe applicability of starch was significantly improved by the use of a non-toxic, biocompatible, and biodegradable other polysaccharide, namely chitosan. The influence of chitosan concentration and electron beam (EB) radiation on the mechanical, processing and microbiological properties of films prepared on the basis of starch was investigated. It turned out that chitosan starch mixtures can be not only good and biodegradable packaging material but also antibacterial by Zhai et al. . In otheIn addition to polysaccharides such as cellulose or chitosan, proteins have also been used to improve the properties of starch. Corradini at al. used zein in thermoplastic starch compositions. Materials based on blends of glycerol plasticized starch and corn protein were prepared by melting processing at 160 °C and then by compression molding. Despite of blend components incompatibility, the use of zein in TPS composites improved the processing properties such lower water sensitivity and lower viscosity .Year by year, more and more attention has been paid to producing only biodegradable blends of biopolymers derived from renewable sources. The results have not always been promising. TPS and PLA blends with glycerol by injection molding and also by compression molding for comparison were prepared. The structure analysis confirmed the weak interaction of the components and heterogenous final material. The higher concentration of TPS caused a decrease in mechanical strength and hydrophobicity . Other rCurrently, crosslinking reactions are most often used in the preparation of starch materials by reactive extrusion. In some studies, on the other hand, films based on crosslinked maize starch were extruded in a reaction catalyzed by chromium octanoate with cellulose acetate as filler and glycerol as plasticizer, respectively. In both cases, crosslinking during reactive extrusion resulted in a film with lower water absorption and better mechanical properties . AnotherAcetylated cassava starch and pea protein isolate were used in the production of blown film. The applied isolate increased the thermal stability, tensile strength, hydrophobicity, and barrier to oxygen and water vapor . ExtrusiThe times when starch was associated only with food are over. This is due to the wide availability and renewal of this biopolymer. Its low production price, non-toxicity, and biodegradability are features that have attracted the attention of non-food industry branches, mainly packaging producers, for many years. Although native or plasticized starch, mainly due to its hydrophilicity and poor mechanical properties, is not an ideal packaging material, various research centers continue to intensify activities toward its processability and functionality. A wide range of physical, chemical, and other modifications makes it possible to increasingly give it properties similar or even competitive to petroleum polymers.Starch and materials based on starch or its derivatives in a system with other natural or synthetic polymers, but only degradable, may constitute the future for sustainable packaging. The commercialization and increase in demand for this type of materials, however, requires certain measures, such as reduced production costs, mainly in biodegradable low-starch blends with polyesters, increased miscibility, as well as eliminated deterioration of mechanical and performance properties in high-starch blends, also those treated with a compatibilizer or based on hydrophobic derivatives. The esterification of starch with fatty acids to increase hydrophobicity and improve thermoplasticity seems to be a significant modification that can increase the usefulness of this polysaccharide in packaging production. It can be found more and more reports on the production of starch-based materials by methods less typically laboratory and more industrial. This is a good prognosis, because not every material obtained, e.g., by casting method, can work under the conditions necessary for effective industrial production.Methods based not only on compression or injection molding and simple extrusion, but such as co-, blown-, or reactive-extrusion are attracting more and more attention. What is very important is that functionalization of starch-based materials toward packaging is developing day by day, not giving way to other more popular polymers.Even if native or plasticized starch itself does not show such processing and mechanical properties to compete with widely distributed synthetic polymers, it is worth emphasizing that their modification, primarily through hydrophobization, will allow one not only to obtain thermoplastic material but more importantly material with increased dispersibility in other hydrophobic thermoplastic materials. As a result, it is possible to design materials with increased biodegradability while maintaining sufficiently good processing and mechanical properties and use pro-ecological modification conditions, ensuring the materials are obtained in accordance with the green chemistry and principles of sustainable development.


Applied Sciences [We have been made aware that Figure 7d of paper  is similSciences . Both fiSciences .The Dentistry Journal Editorial Office apologize to the readers of the Dentistry Journal for any inconvenience caused. To ensure the addition of only high-quality scientific works to the field of scholarly communication, this paper  is retra


Approximate Membership Query structures (AMQs) rely on randomisation for time- and space-efficiency, while introducing a possibility of false positive and false negative answers. Correctness proofs of such structures involve subtle reasoning about bounds on probabilities of getting certain outcomes. Because of these subtleties, a number of unsound arguments in such proofs have been made over the years.In this work, we address the challenge of building rigorous and reusable computer-assisted proofs about probabilistic specifications of AMQs. We describe the framework for systematic decomposition of AMQs and their properties into a series of interfaces and reusable components. We implement our framework as a library in the Coq proof assistant and showcase it by encoding in it a number of non-trivial AMQs, such as Bloom filters, counting filters, quotient filters and blocked constructions, and mechanising the proofs of their probabilistic specifications.by construction. We also show how the proofs about probabilities of false positives for complex AMQs can be obtained by means of verified reduction to the implementations of their simpler counterparts. Finally, we provide a library of domain-specific theorems and tactics that allow a high degree of automation in probabilistic proofs.We demonstrate how AMQs encoded in our framework guarantee the absence of false negatives  Approximate Membership Query structures (AMQs) are probabilistic data structures that compactly implement (multi-)sets via hashing. They are a popular alternative to traditional collections in algorithms whose utility is not affected by some fraction of wrong answers to membership queries. Typical examples of such data structures are Bloom filters , quotiensome loss of precision. For instance, a static points-to analysis may consider two memory locations as aliases even if they are not , still remaining sound. However, it would be unsound for such an analysis to claim that two locations do not alias in the case they do . Even if it increases the number of false positives, a randomised data structure can be used to answer aliasing queries in a sound way—as long as it does not have false negatives [how much precision would be lost if, e.g., a Bloom filter with certain parameters is chosen to answer these queries? Another example, in which quantitative properties of false positives are critical, is the security of Bitcoin’s Nakamoto consensus [Hashing-based AMQs achieve efficiency by means of losing precision when answering queries about membership of certain elements. Luckily, most of the applications listed above can tolerate gatives . But hownsensus  that depnsensus .No-False-Negatives properties, stating that a set-membership query for an element x always returns true if x is, in fact, in the set represented by the AMQ.False Positives by providing a probabilistic bound on getting a wrong “yes”-answer to a membership query, given certain parameters of the data structure and the past history of its usage.Properties quantifying the rate of In the light of the described above applications, of particular interest are two kinds of properties specifying the behaviour of AMQs:Given the importance of such claims for practical applications, it is desirable to have machine-checked formal proofs of their validity. And, since many of the existing AMQs share a common design structure, one may expect that a large portion of those validity proofs can be reused across different implementations.false negatives in a particular AMQ (Bloom filter) has been addressed to some extent in the past [rates of false positives did not extend to such structures. Furthermore, to the best of our knowledge, no other existing AMQs have been formally verified to date, and no attempts were made towards characterising the commonalities in their implementations in order to allow efficient proof reuse.Computer-assisted reasoning about the absence of he past . Howeverreusable program- and specification-level definitions and theorems, implemented in a proof assistant enabling computer-aided verification of a variety of AMQs.In this work, we aim to advance the state of the art in machine-checked proofs of probabilistic theorems about false positives in randomised hash-based data structures. As recent history demonstrates, when done in a “paper-and-pencil” way, such proofs may contain subtle mistakes , 10 due Our Contributions.  The key novel observation we make in this work is the decomposition of the common AMQ implementations into the following components: (a) a hashing strategy and (b) a state component that operates over hash outcomes, together capturing most AMQs that provide fixed constant-time insertion and query operations. Any AMQ that is implemented as an instance of those components enjoys the no-false-negatives property by construction. Furthermore, such a decomposition streamlines the proofs of structure-specific bounds on false positive rates, while allowing for proof reuse for complex AMQ implementations, which are built on top of simpler AMQs [A Coq-based mechanised framework Ceramist, specialised for reasoning about AMQs.A library of non-trivial theorems for expressing closed-form probabilities on false positive rates in AMQs. In particular, we provide the first mechanised proof of the closed form for Stirling numbers of the second kind , Chap. 6A collection of proven facts and tactics for effective construction of proofs of probabilistic properties. Our approach adopts the style of Ssreflect reasoning , 31, andA number of case study AMQs mechanised via Ceramist: ordinary  and couner AMQs . PoweredCounting Blocked Bloom filters and Blocked Quotient filters, and prove corresponding no-false-negatives and false positive rates for all of them. Our case studies illustrate that Ceramist can be repurposed to verify hash-based AMQ structures, including entirely new ones that have not been described in the literature, but rather have been obtained by composing existing AMQs via the “blocked” construction.For ordinary Bloom filters, we provide the first mechanised proof that the probability of a false positive in a Bloom filter can be written as a closed form expression in terms of the input parameters; a bound that has often been mis-characterised in the past due to oversight of subtle dependencies between the components of the structure , 34. Foraxiom-free, and is compatible with Coq 8.11.0 [Our mechanised development  is entir 8.11.0 . It reli 8.11.0  for encoPaper Outline. We start by providing the intuition on Bloom filters, our main motivating example, in Sect. Ceramist is a library specialised for reasoning about AMQ data structures in which the underlying randomness arises from the interaction of one or more hashing operations. To motivate this development, we thus consider applying it to the classical example of such an algorithm—a Bloom filter .not in the Bloom filter, there is a possibility that the query may be answered as positive. Thus a property of direct practical importance is the exact probability of this event, and how it is influenced by the other parameters of the implementation.Bloom filters are probabilistic data structures that provide compact encodings of mathematical sets, trading increased space efficiency for a weaker membership test . Specifim bits , paired with a sequence of k hash functions k indices from m-bit array Assuming an ideal selection of hash functions, we can treat the output of x into the Bloom filter, we can treat each element of the “hash vector” produced from x, we can check that all k bits specified by the hash-vector are raised.A Bloom filter Given this model, there are two obvious properties of practical importance: that of false positives and of false negatives.False Negatives. It turns out that these definitions are sufficient to guarantee the lack of false-negatives with complete certainty, i.e., irrespective of the random outcome of the hash functions. This follows from the fact that once a bit is raised, there are no permitted operations that will unset it.. If  x has been previously inserted into False Positives. This property is more complex as the occurrence of a false positive is entirely dependent on the particular outcomes of the hash functions overlapping sets of indices. That is, after inserting a series of values l distinct items into the Bloom filter will set a particular bit This leads to subtle dependencies that can invalidate the analysis, and have lead to a number of incorrect probabilistic bounds on the event, including in the analysis by Bloom in his original paper . Specifi(Probability of a single bit being set). If the only values previously inserted into i being set is k, reasoning that a false positive for an element k bits corresponding to the hash outputs are set.Bloom then claimed that the probability of a false positive was simply the probability of a single bit being set, raised to the power of et al.  [et al. rectified the analysis by instead interpreting the bits within a Bloom filter as maintaining a set y only tests positive if the random set of indices produced by the hash functions on y is such that y is a subset of the union of Unfortunately, as was later pointed out by Bose et al.  , as the . If the only values inserted into Stirling number of the second kind, capturing the number of surjections from a set of size s to a set of size t.random variables and then propagating this randomness to the results of the other operations. A formal treatment of program outcomes requires a suitable semantics, representing programs as distributions of such random variables. In moving to mechanised proofs, we must first fully characterise this semantics, formally defining a notion of a probabilistic computation in Coq.The key step in capturing these program properties is in treating the outcomes of hashes as To introduce our encoding of AMQs and their probabilistic behaviours in Coq, we continue with our running example, transitioning from mathematical notation to Gallina, Coq’s language. The rest of this section will introduce each of the key components of this encoding through the lens of Bloom filters.Our formalisation represents probabilistic computations using an embedding following the style of the FCF library . We do nA, and is constructed using the standard monadic operators, with an additional primitive Following the adopted FCF notation, a term of type -notation over this monad to allow descriptions of probabilistic computations within Gallina. For example, the following code is used to implement the query operation for the Bloom filter:  In the above listing, we pass the queried value . Then, having mapped our input into a sequence of indices, we can query the Bloom filter for membership using a corresponding deterministic operation We implement a Haskell-stylesyntax of the probabilistic query and has no actual meaning without a separate interpretation.Using the code snippet above, we can define the query operation A produces 1.Thus, given a Gallina term of type y monad , which dy monad , 2, and e  before stating its probability bound. Therefore, we hide this evaluation process behind a notation that allows stating probabilistic properties in a form closer to their mathematical counterparts: This mapping from computations to distributions must be done to a program v is an arbitrary element in the support of the distribution induced by e. Finally, we introduce a binding operator Above, ) in Coq as a binary vector of a fixed length m, using Ssreflect ’s  We define the deterministic components of the Bloom filter implementation as pure functions taking an instance ofand a series of indices assumed to be obtained from earlier calls to the associated hash functions:We define the state of a Bloom filter . For any Bloom filter state x into (Probability of Flipping a Single Bit). For a vector of hash functions k, after inserting a series of l distinct values m bits, the probability of its any index i being set is is a simple embedding of the pure functioninto a probabilistic computation.. After having inserted a series of l distinct values y returning true is given as the first axiom-free mechanised proof for the closed form for Stirling numbers of the second kind [The proof of this theorem required us to provide nd kind .. In general, structuring AMQ operations as manipulations with hash outputs via pure deterministic functions allows us to decompose reasoning about the data structure into a series of specialised properties about its deterministic primitives and a separate set of reusable properties on its hash operations.In the definitions above, we used the output of the hashing operation as the bound between the deterministic and probabilistic components of the Bloom filter. For instance, in our earlier description of the Bloom filter query operation in Sect. seen hashes learnt by hashing previously observed values, we represent a state of a hash function from elements of typeto a range  The state is paired with a hash function generating uniformly random outputs for unseen values, and otherwise returns the value as from its prior invocations:  A hash vector is a generalisation of this structure to represent a vector of states of k independent hash functions:  The corresponding hash operation over the hash vector, We encode hash operations within our development using a random oracle-based implementation. In particular, in order to keep track of have been seen before or not. For example, if we knew that a value x had not been seen before, we would know that the possibility of obtaining any particular choice of a vector of indices would be equivalent to obtaining the same vector by a draw from a corresponding uniform distribution. We can formalise this intuition in the form of the following theorem:This random oracle-based implementation allows us to formulate several helper theorems for simplifying probabilistic computations using hashes by considering whether the hashed values (Uniform Hash Output). For any two hash vectors k, a value x that has not been hashed before, and an output vector m obtained by hashing x via x to have already seen. In these cases, if we know the exact indices a value hashes to, we can prove a certainty on the value of the outcome:Similarly, there are also often cases where we are hashing a value that we (Hash Consistency). For any hash vector x, if x to outputs x again will certainly produce deterministic components of the data structure. This decomposition is not just applicable to the case of Bloom filters, but can be extended into a general framework for obtaining modular proofs of AMQs, as we will show in the next section.By combining these types of probabilistic properties about hashes with the earlier Bloom filter operations, we are able to prove the prior theorems about Bloom filters by reasoning primarily about the core logical interactions of the Zooming out from the previous discussion of Bloom filters, we now present Ceramist in its full generality, describing the high-level design in terms of the various interfaces it requires to instantiate to obtain verified AMQ implementations.The core of our framework revolves around the decomposition of an AMQ data structure into separate interfaces for hashing (AMQHash) and state (AMQ), generalising the specific decomposition used for Bloom filters (hash vectors and bit vectors respectively). More specifically, the AMQHash interface captures the probabilistic properties of the hashing operation, while the AMQ interface captures the deterministic interactions of the state with the hash outcomes.The AMQHash interface generalises the behaviours of hash vectors Sect.  to provie.g.,) by treating them as opaque parameters: using a parameter would be, while for a hash vector this would instead be.The interface first abstracts over the specific types used in the prior hashing operations :  Then, to abstractly capture the kinds of reasoning about the outcomes of hash operations done with Bloom filters in Sect.  These components are then combined together to produce more abstract formulations of the previous Theorems To use this hash state in probabilistic computations, the interface assumes a separate probabilistic operation that will take the hash state and randomly generate an output . There exists a probability x that is unseen, and an output x via x to . For any AMQ hash state x, if x to an output x again will certainly produce Proofs of these corresponding properties must also be provided to instantiate the AMQHash interface. Conversely, components operating over this interface can assume their existence, and use them to abstractly perform the same kinds of simplifications as done with Bloom filters, resolving many probabilistic proofs to dealing with deterministic properties on the AMQ states.of a particular hashing operation.Building on top of an abstract AMQHash component, the AMQ interface then provides a unified view of the state of an AMQ and how it deterministically interacts with the output typeadd and query operations of an AMQ:  In the case of Bloom filters, these would be instantiated with the,andoperations respectively . For a state s with sufficient capacity, inserting any hash output s viawill produce a new state (AMQ query preservation). For any AMQ state s with sufficient remaining capacity, if queries for a particular hash output s viahappen to return true, then inserting any further outputs s will return a state for which queries for still return true.sufficient to ensure the No-False-Negatives property standard of most AMQs:Even though these assumptions seemingly place strict restrictions on the permitted operations, we found that these properties are satisfied by most common AMQ structures. One potential reason for this might be because they are in fact . For any AMQ state s, a corresponding hash state x into s, followed by a series x is always true. That is, ,, andare generalisations of the probabilistic wrappers of Bloom filters . As mentioned before, the add operation increments counters rather than setting bits, and the query operation treats counters greater than 0 as raised.First, as the Counting Bloom filter uses the same hashing strategy as the Bloom filter, the hash interface can be instantiated with the Hash Vector structure used for the Bloom filter, entirely reusing the earlier proofs on hash vectors. Next, in order to instantiate the AMQ interface, the state parameter can be defined as a vector of bounded integers, all initially set to 0: l further inserts by ensuring that each counter has at least k is the number of hash functions used by the data structure).To prevent integer overflows, the counters in the Counting Bloom filter are bounded to some range The add operation can be shown to be monotone on the value of any counter when there is sufficient capacity Property . The remAs the observable behaviour of Counting Bloom filter almost exactly matches that of the Bloom filter, it seems reasonable that the same probabilistic bounds should also apply to the data structure. To facilitate these proof arguments, we provide the AMQMap interface that allows the derivation of probabilistic bounds by reducing one AMQ data structure to another.The AMQMap interface is parameterised by two AMQ data structures, AMQ A and B, using the same hashing operation. It is assumed that corresponding bounds on False Positive rates have already been proven for AMQ B, while have not for AMQ A. The interface first assumes the existence of some mapping from the state of AMQ A to AMQ B, which satisfies a number of properties: In the case of our Counting Bloom filter example, this mapping would convert the Counting Bloom filter state to a bit vector by mapping each counter to a raised bit if its value is greater than 0. To provide the of the false positive rate boundary, the AMQMap interface then requires the behaviour of this mapping to satisfy a number of additional assumptions:(AMQ Mapping Add Commutativity). Adding a hash output to the AMQ B obtained by applying the mapping to an instance of AMQ A produces the same result as first adding a hash output to AMQ A and then applying the mapping to the result.(AMQ Mapping Query Preservation). Applying B’s query operation to the result of mapping an instance of AMQ A produces the same result as applying A’s query operation directly.In the case of reducing Counting Bloom filters (A) to Bloom filters (B), both results follow from the fact that after incrementing the some counters, all of them will have values greater than 0 and thus be mapped to raised bits.Having instantiated the AMQMap interface with the corresponding function and proofs about it, it is now possible to derive the false positive rate of Bloom filters for Counting Bloom filters for free through the following generalised lemma:. For any two AMQs A, B, related by the AMQMap interface, if the false positive rate for B after inserting l items is given by the function f on l, then the false positive rate for A is also given by f on l. That is, in terms of probabilities: We have, until now, avoided discussing details of how facts about the probabilistic computations can be composed, and thereby also the specifics of how our proofs are structured. As it turns out, most of this process resolves to reasoning about summations over real values as encoded by Ssreflect ’s bigop library. Our development also relies on the tactic library by Martin-Dorel and Soloviev .Pattern to refer to a general pattern our library supports by means of a dedicated Coq tactic, while Lemma will refer to standalone proven equalities.In this section, we outline some of the most essential proof principles facilitating the proofs-by-rewriting about probabilistic sums. While most of the provided rewriting primitives are standalone general equality facts, some of our proof techniques are better understood as combining a series of rewritings into a more general rewriting pattern. To delineate these two cases, will use the terminology cf.  Sect. operator. Therefore, when decomposing a probabilistic property into smaller subproofs, we must rely on its semantics that is defined for discrete distributions as follows:When stating properties on outcomes of a probabilistic computation separately by applying subsequent rewritings to each factor on the right-hand side of the above equality.Here, by Having resolved a property into our normal form via a tactic implementing Pattern Sequential Composition. When reasoning about the properties of composite programs, it is common for some subprogram e to return a probabilistic result that is then used as the arguments for a probabilistic function f. This composition is encapsulated by the operation entclass1pt{minimaSince the return operation is defined as a delta distribution with a peak at the return value .Notice that, without loss of generality, Pattern Plausible Statement Sequencing. One common issue with the normal form, is that, as each statement is evaluated over the entirety of its support, some of the dependencies between statements are obscured. That is, the outputs of one statement may in fact be constrained to some subset of the complete support. To recover these dependencies, we provide the following theorem, that allows reducing computations under the assumption that their inputs are plausible:(Plausible Sequencing). For any computation sequence x is amongst plausible outcomes of i.e., Plausible Outcomes. As was demonstrated in the previous paragraph, it is sometimes possible to gain knowledge that a particular value v is a plausible outcome for a composite probabilistic computation v. However, we can now turn this inequality into a conjunction of inequalities for individual probabilities, thus getting more information about the intermediate steps of the computation:If  This transformation is possible due to the fact that probabilities are always non-negative, thus if a summation is positive, there must exist at least one element in the summation that is also positive.Summary of the Development. By composing these components together, we obtain a comprehensive toolbox for effectively reasoning about probabilistic computations. We find that our summation patterns end up encapsulating most of the book-keeping associated with our encoding of probabilistic computations, which, combined with the AMQ/AMQHash decomposition from Sect.  We label the factors to be rewritten as (a)–(e) for the convenience of the presentation, indicating the correspondence to the components of the statement (a) and (b) as follows:To showcase the fluid interaction of our proof principles in action, let us consider the proof of the generalised No-False-Negatives Theorem x to x in (d) must return Here, entclass1pt{minimaFinally, as i) a library of bounded-length data structures, enhancing MathComp ’s [ii) a library of probabilistic computations, extending the infotheo probability theory library [iii) the AMQ interfaces and instances representing the core of our framework described in Sect. The Ceramist mechanised framework is implmented as library in Coq proof assistant . It consComp ’s  support library  with defet al.[Alongside these core components, we also include four specific case studies to provide concrete examples of how the library can be used for practical verification. Our first two case studies are the mechanisation of the Bloom filter  and the et al., also pret al.. Our finet al.. The sizprogressively decreases, with around a 50% reduction in the size from our initial proofs of Bloom filters to the final case-studies of different Blocked AMQs instances.Of particular note, in effect due to the extensive proof reuse supported by Ceramist, the proof size for each of our case-studies A quotient filter  is a typquotienting, whereby a single p-bit hash outcome is split into two by treating the upper q-bits (the quotient) and the lower r-bits (the remainder) separately. Whenever an element is inserted or queried, the item is first hashed over a single hash function and then the output quotiented. The operations of the quotient filter then work by using the q-bit quotient to specify a bucket of the hash table, and the r-bit remainder as a proxy for the element, such that a query for an element will succeed if its remainder can be found in the corresponding bucket.The internal operations of a quotient filter build upon a fundamental notion of single hash function, rather than a vector of hash functions, which is used by the Bloom filter variants . Therefore, it is then possible to reduce the event of a false positive in a quotient filter to the event that at least one in several draws from a uniform distribution produces a particular value. We encode quotient filters by instantiating the AMQHash interface from Sect. ts Sect. . The siz. For a hash-function l unseen distinct values y returning true is given by: m independent Bloom filters, using an additional “meta”-hash operation to distribute values between the elements. When querying for a particular element, the meta-hash operation would first be consulted to select a particular instance to delegate the query to.Blocked Bloom filters are a cawrt. composition of programs and proofs.While prior research has only focused on applying this blocking design to Bloom filters, we found that this strategy is in fact generic over the choice of AMQ, allowing us to formalise an abstract Blocked AMQ structure, and later instantiate it for particular choices of “basic” AMQs. As such, this data structure highlights the scalability of Ceramist i) a multiplexed-hash component, parameterised over an arbitrary hashing operation, and (ii) a blocked-state component, parameterised over some instantiation of the AMQ interface. The multiplexed hash captures the relation between the meta-hash and the hashing operations of the basic AMQ, randomly multiplexing hashes to particular hashing operations of the sub-components. We construct a multiplexed-hash as a composition of the hashing operation H used by the AMQ in each of the m blocks, and a meta-hash function to distribute queries between the m blocks. The state of this structure is defined as pairing of m states of the hashing operation H, one for each of the m blocks of the AMQ, with the state of the meta-hash function. As such, hashing a value v with this operation produces a pair of type v over the meta-hash to select a particular block, and the second element is produced by hashing v again over the hash operation H for this selected block. With this custom hashing operation, the state component of the Blocked AMQ is defined as sequence of m states of the AMQ, one for each block. The insertion and query operations work on the output of the multiplexed hash by using the first element to select a particular element of the sequence, and then use the second element as the value to be inserted into or queried on this selected state.Our encoding of Blocked AMQs within Ceramist is done via means of two higher-order modules as in Fig. Having instantiated the data structure as described above, we proved the following abstract result about the false positive rate for blocked AMQs:. For any AMQ A with a false positive rate after inserting l elements estimated as f(l), for a multiplexed hash-function l distinct values m instances of A, for any unseen y returning true is given by: We instantiated this interface with each of the previously defined AMQ structures, obtaining the Blocked Bloom filters, Counting Blocked Bloom filters and Blocked Quotient filter along with proofs of similar properties for them, for free.Proofs About AMQs. While there has been a wealth of prior research into approximate membership query structures and their probabilistic bounds, the prevalence of paper-and-pencil proofs has meant that errors in analysis have gone unnoticed and propagated throughout the literature.et al.  [et al.  [et al.  [et al.  [The most notable example is in Bloom’s original paper, whereinet al.  , their oet al.  , who avoet al.  , 41, 46 et al.  ’s analyset al.   providedMechanically Verified Probabilistic Algorithms. Past research has also focused on the verification of probabilistic algorithms, and our work builds on the results and ideas from several of these developments. The ALEA library tackles the task of proving properties of probabilistic algorithms [et al. ’s Polaris  [orithms , howeverorithms , represeorithms  was deveolaris   library olaris  , using aolaris  . While tProofs of Differential Privacy. A popular motivation for reasoning about probabilistic computations is for the purposes of demonstrating differential privacy. Barthe et al. ’s CertiPriv framework [et al.  [amework  extends et al.   have devThe key properties of Approximate Membership Query structures are inherently probabilistic. Formalisations of those properties are frequently stated incorrectly, due to the complexity of the underlying proofs. We have demonstrated the feasibility of conducting such proofs in a machine-assisted framework. The main ingredients of our approach are a principled decomposition of structure definitions and proof automation for manipulating probabilistic sums. Together, they enable scalable and reusable mechanised proofs about a wide range of AMQs.


Grafting is a technique used for millennia for vegetative propagation, especially in perennial fruit crops. This method, used on woody and herbaceous plants, can improve several agronomic characteristics, such as yield or vigor, as well as tolerance to biotic and abiotic stresses. However, some scion/rootstock combinations suffer from poor graft compatibility, i.e., they are unable to form and/or sustain a successful graft union. Identifying symptoms of graft incompatibility is difficult because they are not always present in the first years after grafting and in most cases the causes of incompatibility are still poorly understood. Studies of changes in transcript abundance during graft union formation indicate that grafting responses are similar to responses to wounding and include the differential expression of genes related to hormone signaling, oxidative stress, formation of new vascular vessels, cell development, and secondary metabolites, in particular polyphenols. This review summarizes current knowledge of the changes in transcript abundance, redox status and metabolites accumulation during graft union formation and in cases of graft incompatibility. The goal of this review is to discuss the possibility of identifying marker transcripts, enzyme activities and/or metabolites of grafting success and graft compatibility which could be used to score grafting success for genetic research and in breeding programs. We highlight gaps in current knowledge and potential research directions in this field. Grafting is a traditional horticultural technique that manipulates plant wound healing mechanisms to join together two genotypes to form a composite plant. Grafting is used for different reasons: for example, to control vegetative multiplication, reduce the time to obtain the fruits, change cultivars quickly, increase or decrease the size, or provide tolerance to biotic or abiotic stresses , which requires rapid wound closure to prevent water loss and pathogen entry. Polymerized phenolic compounds such as suberin and lignin accumulate to act as a physical and antimicrobial barrier at the site of wounds. Wounding triggers an oxidative stress burst, changes to metabolism, wound-related hormone signaling and the initiation of defense responses such as the induction of pathogenesis-related proteins. During graft union formation, there is a proliferation of parenchymal cells, to form the callus which will serve as a bridge between the two tissues. Then, there is the differentiation of the cambial cells into vascular vessels, which begins with the formation of phloem vessels in some herbaceous plants [from 3 days after grafting (DAG)] and then xylem vessels  and auto-grafting (when the same plant is grafted with itself) are only used in scientific study  between two hetero-grafts and the scion homo-graft was first done in grapevine  could be a marker of graft compatibility, being expressed at a lower level, and in lower protein concentration and activity in incompatible callus grafts  . This has led to the study of the role of PHENYLALANINE AMMONIA LYASE (PAL), the first and committed step in the phenyl propanoid pathway, in graft union formation and graft incompatibility. In N. benthamiana/Arabidopsis at 2 h after grafting, and 1, 3, 5, and 7 DAG and compared to gene expression in intact stems  rapidly results in the formation of a strong carbon gradient from the carbon-rich scion to the carbon-starved rootstock, which disappears once the phloem has reconnected. This asymmetry triggers the differential expression of the sugar-responsive genes above and below the graft union , such as singlet oxygen, superoxide, hydrogen peroxide, and hydroxyl radicals, which can cause severe damage to cell structure and functions. Plant have complex antioxidant system to control ROS via non-enzymatic  and enzymatic antioxidants . The high expression of genes , only one study has quantified PAL activity at the graft interface, which was 2-fold higher than to the surrounding woody tissues 28 DAG in homo-grafts of grapevine  of clones of Vaccinium spp. and pear trees), but this did not affect scion metabolite concentrations (Hudina et al., The most famous example of a secondary metabolite involved in graft incompatibility is prunasin, which has been long known to be responsible for graft incompatibility in pear/quince grafts (Gur et al., Eucalyptus gunnii 20 DAG (De Cooman et al., Several phenolic compounds, such as gallic acid, gentisic acid, ellagic acid, p-coumaric acid, catechin, and quercetin-3-glucoside, were found in high concentration in less compatible combinations compared to more compatible combinations in micro-grafts of In both cherries and apricots rootstock polyphenol concentration differs between different genotypes and it seems like the rootstock alters scion polyphenol concentrations just above the graft union (Usenik and Stampar, Uapaca kirkiana 3 years after grafting; both total soluble and cell wall bound phenol concentrations were higher at the graft interface than the surrounding woody tissues for some, but not all, of the homo- and hetero-grafts studied (Mng'omba et al., Total soluble and cell wall bound phenol concentrations were studied at the graft interface of homo- and hetero-grafts of U. kirkiana grafts (Mng'omba et al., In addition to the quantification of metabolites in bulk samples, the accumulation of polyphenols at the graft interface has been studied using imaging methods; the visualization of necrosis areas and callus development provides knowledge of the tissue specific location of different metabolites. For example, flavonoid accumulation has been studied in callus grafts (Pina and Errea, As described above, there have been a number of studies into the accumulation of phenolic compounds associated with graft union formation and these studies have highlighted the complexity of the metabolite responses of different species. It is difficult to make generalities about the metabolite response to grafting because different samples have been taken, such as, entire stems vs. just the phloem, cambium and/or bark. Many of the results in the literature are difficult to interpret because control samples are missing. Similarly the metabolite profile of woody tissues appears to change over time suggesting that a marker of graft incompatibility may only be valid at a certain developmental stage.It is known that graft incompatibility is under genetic control (Salesses and Al Kaï, GL drafted and SC revised the manuscript. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The use of synthesized natural starches for the sizing process in fabric production is primarily an environmental contribution. Synthesized corn starch is environmentally friendly and productive, showing good results in cotton yarn sizing. Acrylamide (AA) and 2-hydroxyethyl methacrylate (HEMA) were applied for the grafting process of corn starch, and the initiators azobisisobutyronitrile (AIBN), potassium persulfate (KPS), and benzoyl peroxide (BP) were chosen to form the grafted monomers more effectively. The application of synthesized corn starch has been confirmed, especially with the AIBIN initiator in the grafting process of HEMA onto starch. The FTIR analysis confirmed that new and efficient products for sizing cotton yarns based on natural raw material (corn) were developed. The research showed that the synthesized corn starch improved physical-mechanical yarn properties and abrasion resistance and reduced yarn surface hairiness. Ultrasonic desizing of yarn and the use of a lower size concentration led to better results than desizing by washing, and the Tegewa numbers confirmed that the desizing process was successful. Sizing is one of the most complex, but also one of the most expensive steps in fabric production, unfortunately still one of the biggest wastewater polluters in the textile industry. Cotton warp yarn sizing cannot usually be avoided if the quality and economic production of fabrics is conditional. Sizing increases warp yarn strength, abrasion resistance, and reduces surface hairiness and static electricity, all of which are crucial parameters for achieving necessary conditions in fabric production. When warp yarn sizing was introduced, natural starches, such as corn, potato, wheat, etc. were applied. Their disadvantage was the size of molecules, which hardly penetrated the interstices of the threads, viscosity instability when changing the temperature, formation of a rigid film on the thread surface, decrease in yarn elasticity, rapid rotting, gel appearance, formation of foam in the size box, uneven size pick up, size removal in the weaving process, higher number of breaks, desizing with microorganisms, and inability to recycle ,2,3.The modification of natural starches reduces or even eliminates all deficiencies of natural starches. Starch modification reduces retrogradation, paste gelling tendencies and gel syneresis, improves paste clarity and gloss, as well as paste and gel texture. In this way, starch adhesion is improved, and a protective film is formed around the thread, which is extremely important for hydrophobic synthetic fibres . The modChemical modification of starch includes polymeric molecules of starch granules in their native form. Modification is achieved by derivatization such as etherification, esterification, and thus crosslinking, oxidation, catonization, and starch grafting. There is a trend of combining different types of chemical treatments to create new types of modifications ,18,19,20With the use of chemical agents, the quality of the fabric and the cost-effectiveness of production increased significantly, while the negatives of synthetic agents remained in the background, such as: environmental pollution, danger to human health, aggressiveness of the agents significantly affects the respiratory tracts of the workers who are daily present during the sizing process, destroying parts in the size box such as rollers, bearings, measuring devices and box walls. Despite this fact, the textile industry applies chemical sizing agents and has almost completely replaced natural modified agents. However, improvements in the sizing process are now reflected in the development and application of new sizing agents, all with the aim of achieving the most economical, efficient and environmentally friendly product ,30.Modification of natural starches reduces or almost eliminates all deficiencies of natural starches. As environmentally friendly products, they should gradually replace fully synthetic sizing agents such as polyvinyl alcohol (PVA), carboxyl methyl cellulose (CMC), polyacrylate (PA), and other synthetic agents used in the sizing process today ,32,33.The selection of sizing agents, the conditions and methods of sizing, and the optimization of size pick-up on the yarn constitute one of the greatest challenges for technologists in the sizing and weaving process. It is often very difficult and almost impossible to determine the appropriate recipe for each type of yarn due to the deviation of the properties of the yarn, the types and proportions of sizing agents, the sizing and weaving conditions.The synthesis of modified starches and the verification of their efficacy itself is a type of activity that requires knowledge of the chemical and mechanical properties of the chemicals from which new active substances are synthesised in particular, as well as the textile materials to which these active substances are applied in order to fulfil their function under certain conditions in the weaving process .As the size pick-up on the yarn increases, the number of breaks decreases significantly up to a certain limit when it starts to rise again , indicatThe investigation was carried out on cotton yarns with counts of 20 tex, 30 tex, 20 × 2 tex and 30 × 2 tex. 2H5OH , and sodium carbonate—Na2CO3 . The following monomers were employed: -3H5NO ,acrylamide (AA) C-6H10O3 .2-hydroxy-ethyl methacrylate (HEMA) CFor the purposes of this research the following active products were employed.: corn starch , hydrochloric acid—HCl , ethyl alcohol (ethanol)—C-azobisisobutyronitrile (AIBN) i.e., ) 99% ,-2S2O8 ,potassium persulfate (KPS) K-6H5CO)2O2  [benzoyl peroxide (BP)  .The following initiators were used in the grafting process: −1 was conducted. Yarn hairiness was tested on a Zweigle G 565 instrument  for yarn hairiness testing according to standard ASTM D 5674-01. Abrasion resistance of the yarn was measured on the Zweigle G551 yarn abrasion tester . The yarn sizing process was carried out on an innovative laboratory sizing machine adapted to industrial conditions, University of Zagreb Faculty of Textile Technology, Zagreb, Croatia . MicroscThe HPLC method (high pressure liquid chromatography) was implemented to examine the residual amounts of unreacted monomer in the copolymer. Tests were carried out on the device Agilent Series 1100 HPLC  with diode-array detector, DAD 1200 Series. The detection wavelength was 205 nm. The ZORBAX Eclipse XDB-C18 column , 4.6 × 250 mm, 5 μm was used. The effluent was methanol, the flow rate was 1 mL/min, the column was thermostated at 25 °C and the injected volume was 20 μL. Monomer standards were prepared by single weighing of the sample with diluted methanol.Apparent viscosity was determined on the rotational viscometer “Visco Basic Plus” . Starch solutions were prepared in a way that the starch was dispersed in distilled water, after which the solution was heated to 100 °C, with stirring at a speed of 150 rpm. When measuring viscosity, a spindle marked R3 was used, with a spindle speed of 60 rpm. Measurements were performed at different temperatures: 40 °C (reaching time 15 min), 60 °C (reaching time 20 min), 85 °C (reaching time 30 min).Mn, Mw, Mz, D) were determined using a GPC Agilent 1100 Series gel permeation chromatograph  using a 1200 Series  differential refractometer (RID detector) as a detector. A Zorbax PSM 300 column, 250 × 6.2 mm, 5 μm with a nominal molar mass range of 3 × 103–3 × 105 g/mol was used. In order to construct a calibration diagram for the purpose of quantitative processing of gel-chromatograms of the tested hydrolysed starch copolymers, calibration of Zorbax PSM-300 gel column was performed using dextran samples  with narrow molar mass distributions. Dextran standards, of known molar masses and the same concentrations as for the samples, were applied in the same way as the samples. Redistilled water was used as eluent, at a flow rate of 1 mL/min. The column was thermostated at 25 °C and the injected volume of the sample solution was 20 μL. Solutions of copolymers in redistilled water at a concentration of 4.5 mg/mL were used for analysis, which were filtered through a 0.45 μm filter before measurement.Mean molar masses and molar mass distribution (The size pick-up (D) on the yarn was determined by mass technology. During the sizing process, percentages of the copolymer solution in the water (concentration) for the single yarn were 5%, 10%, 15%, and for the ply yarn: 1%, 3%, and 5%, adapted to industrial conditions.bd denotes mass before desizing (g), and mad mass after desizing (g).Desizing of sized yarn samples was performed using a non-ionic detergent, Lavan NH , concentration 2 g/L, with a ratio of 1:30 in the Ahiba Linites apparatus. The aqueous solution of this agent was heated at 60 °C for 5 min, before a sized yarn sample was added and treated for 30 min at the same temperature. Finally, the sample was washed abundantly with water and air-dried. Furthermore, one part of the experimental desizing was carried out applying ultrasonic energy with an ultrasonic bath . The frequency of applied ultrasonic oscillations was 40 kHz, power used was 150 W, time 30 min, and temperature 60 °C. The degree of desizing (%) was obtained by gravimetric calculation based on mass differences:To prepare the samples before measurement, they were conditioned in a thermal chamber with the following conditions: temperature 20 ± 1 °C, humidity 65 ± 2%.3. Finally, the solution was supplemented with ethanol to increase the content to 1 L. The raw material was immersed in this solution and kept for 1 min, after which it was washed in cold water. This was followed by the absorption of excess water with the filter paper and a quick comparison with the Tegewa scale [The Tegewa method was used to identify residual starch derivatives with the aid of iodine solution. The iodinated solution was prepared by dissolving 10 g of potassium iodide in 100 mL of water, followed by the addition of 0.65 g of iodine and dilution with water to an amount of 800 cmwa scale .The hydrolysis process ,39 was cThe grafting process with the initiators AIBN, KPS, BP ,41,42 waThe reaction product (hydrolysed starch grafted with AA) was precipitated in 100 mL of ethanol. After straining, the precipitate was washed for 10 min with ethanol at room temperature and then with ethanol-water solution in a ratio of 80:20, 3–5 times . Finally−1 is observed, which stems from O–H valence vibrations as well as a smaller peak at 2925 cm−1, which is attributable to the C–H valence vibration. Wave numbers at about 1153, 1078 and 1023 cm−1 describe C–O–C stretching (triplet of starch) [−1 resting on a peak occurring at about 3670 cm−1. Peaks at about 570, 764, 860, and 920 cm−1 (vibrations of the –OH group) in grafted starch change in intensity and shape, indicating that OH starch groups changed during the reaction. Thus, the presence of these additional peaks in the case of grafted starch as compared to hydrolysed starch confirms the successful grafting of poly (acrylamide) chains onto starch [−1, valence vibrations of C=C double bonds at 1650 cm−1, vibrations of C–H bond; νs (CH3) at 2928 cm−1, and the valence vibrations of the OH group at about 3420 cm−1. Vibrations of the ring of the aromatic core were observed at 1600, 1505, and 1470 cm−1. Asymmetric and symmetric stretching vibrations of the methyl group were observed at 1455 and 1380 cm−1 [ starch) . In the o starch . The FTI380 cm−1 .The amounts of residual AA and HEMA monomer in the copolymer samples after grafting onto hydrolysed starch are shown in After chromatography of a suitable sample of starch copolymer, depending on the detector used (RID), ChemStation software provides an appropriate chromatogram with characteristic chromatographic parameters. The program offers the possibility to activate the GPC software and transfer the obtained data to process the chromatograms and analyse the molecular masses of each separated fraction of the analysed polymer. About 0.2 g of powdered, dried copolymer was used for analysis. The sample was extracted with 10 mL of methanol at room temperature for 48 h with occasional stirring. The extracts were filtered through a 0.45 μm filter and used for HPLC analysis.GPC software was used to process the chromatograms of the starch copolymer samples. Mw > Mn , i.e., they are polydisperse systems, the rule applies: the higher the difference between Mw and Mn, the more polydisperse the system is  when longer chains or their aggregates are moved . Table 5Microscopic representation of starch copolymer solution can help to understand the rheological behaviour of macromolecular chains in the solution. Corn starch granules have an oval and spherical shape, some of the granules have an irregular shape with individual sharp edges the size of which ranges from 2–30 μm . The layers are not visible and show a three-pointed crack or a bright cavity in the middle. Small grains (2–8 μm) are round and interconnected . There iStarch granules become thinner and more easily attacked by hydrogen ions, which agrees with the fact that amorphous regions of starch granules are primarily degraded by acid hydrolysis. Since the amorphous regions are mainly located within the starch granules and the crystalline regions mainly in the outer part of the starch granules, the starch granules become thinner during the first acid hydrolysis phase and break up at a later stage. Starch properties depend on the contents of amylose and amylopectin, but also on other components contained in the starch granule, such as phosphates, lipids, phospholipids, etc. However, amylopectin, as a basic starch component, has a dominant effect on starch properties ,53. The During the disintegration of starch granules, the release of amorphous amylose first occurs, building a three-dimensional network beyond starch granules and inhibits further swelling of starch granules. In addition to amylose, the present lipids also inhibit swelling. Although amylose contributes only slightly to the viscosity of the starch solution after granule disintegration, the viscosity increases with increasing amylose content after cooling of the starch solution, which is explained by the crystallization of amylose and the formation of a gel structure.It is known that starch solution is retrograded during the starch dormant state, which is one of the reasons for the poor performance. During starch retrogradation, external short side chains of amylopectin are rapidly transformed from the ball into a helix structure by associating the external short chains and by forming a B-type crystalline structure, whereas amylose forms double helix associates. Starch retrogradation is also influenced by the presence of phosphates, lipids and phospholipids, temperature, solution concentration, pH of solution and the presence of some ingredients. Retrogradation accelerates with increasing concentration and decreasing temperature of the solution. Very short chains (degree of polymerization of 6–9) suppress starch retrogradation .For the purpose of this research, starch derivatives were prepared in concentrations of 1%, 3%, 5%, 10%, and 15%. During the preparation of the solution, it was observed that the solution was opalescent and that at lower concentrations up to 3%, the hydrolysed corn starch solution acted almost like a Newtonian fluid.This means that starch macromolecules are sufficiently distant from each other to prevent strong physical cross-linking, and that finally formed bonds are easily broken by mechanical forces and fail to be formed again in a relatively short time in the tested range of oscillation frequencies. It is known that the solubility of natural starch increases significantly with hydrolysis, i.e., polar vinyl monomer copolymerization .Viscosity as an indicator of the size of starch molecules assumes that their higher values imply larger macromolecules and subsequently lower solubility and higher viscosity . The high grafting content will now disrupt the intermolecular bonds of the starch chains and increase hydrophobicity. In the constellation of relations between hydrophilic and hydrophobic interactions, the influence of secondary chemical bonds, grafted macromolecules show specific behaviour in solution, which is reflected in the viscosity and also in the binding to cotton yarn in its impregnation processes. It is noticeable that the viscosity of all solutions of copolymers of HEMA monomers has a slightly higher value, which implies the assumption that grafting with this monomer partially reduces the solubility of hydrolysed starch. Taking into account that the same concentrations of hydrolysed starch solution had a slightly lower viscosity, it can be argued that starch grafting with vinyl monomers increased the viscosity of the solution, i.e., the size of the hydrolysed starch molecules increases during grafting. The presence of grafted chains in the molecular structure of starch causes significant changes in the behaviour of starch in aqueous solutions. In addition to loosening the starch structure, grafted chains appear to be able to associate molecules. Finally, the chains grafted onto the hydrolysed starch increase the molar mass and lead to possible cross-linking, since it is possible to create different types of secondary chemical bonds . It is noticeable that, with decreasing starch concentration, the viscosity declines as expected . The infFor example, the hydrolysed starch designated as HS-5 at 40 °C had a viscosity of 38.8 mPa·s, while the highest value for the same concentration was observed for the grafted hydrolysed starch designated as HS-HEMA-5, which at 40 °C had a viscosity of 44.8 mPa·s; it is also similar at other temperatures, so HS-5 had a viscosity of 57.1 mPa·s at 60 °C, while the highest value for the same concentration was observed for the grafted hydrolysed starch designated as HS-HEMA-5, which had a viscosity of 62.0 mPa·s at the same temperature. By increasing the viscosity, the surface size pick-up on the yarn is higher in contrast to the low viscosity, which at the same time assumes a lower size pick-up on the surface of the yarn, but probably more uniform and larger in the interior, which is an additional necessary requirement in the sizing process. As a rule, higher size temperature means lower viscosity, which is not the case with the applied starch, but it is certain that higher temperature allows a faster movement of size molecules, and thus a higher degree of overcoming adhesion forces and a better adsorption of the size to the fibres in the yarn. Considering the mentioned effects, it can be claimed that the effective yarn sizing process depends on: concentration, viscosity, size temperature, recipe, size dormant state, and on the sizing conditions such as: yarn tension, sizing speed, the pressure of the squeeze rollers, drying method and drying temperature, etc. The current mutual influence of these parameters, antagonism or synergism, will determine sizing efficiency and quality. By increasing the size concentration  the size pick-up on the yarn increases in all samples . HydrolyStarch hydrolysis caused an increase in the breaking forces in all samples. Starch grafting caused an additional increase in breaking forces. The HEMA grafted starch achieves better results than AA in terms of breaking forces for all yarn types, which indicates its correct arrangement and good adhesion both on the surface and inside the yarn. Due to a higher concentration, the breaking force was higher for the single yarn  and the plied yarn , but elongation at break mostly decreased .One of the aims of yarn sizing is to increase the abrasion resistance of the yarn so that the yarn running through the elements of the weaving machine  can withstand without breaking , as showGrafted starch proved to be an efficient product with regard to abrasion resistance, especially HS-HEMA, which can be sought in its hydrophobicity. The waterproof behaviour or more difficult dissolution of HS-HEMA starch decreases if more monomers are grafted on it. High grafting content disrupts the intermolecular bonds of starch chains and increases hydrophobicity. In the constellation of relations between hydrophilic and hydrophobic interactions, the influence of secondary chemical bonds, grafted macromolecules show specific behaviour in solution, which is reflected in viscosity and then in binding to cotton yarn in impregnation processes. It is noticeable that the viscosity of the copolymer solution of the HEMA monomer had a slightly higher value, which implies the assumption that grafting with this monomer partially reduces the solubility of hydrolysed starch. This resulted in a better yarn surface protection.One of the goals of sizing is to reduce yarn hairiness, which has negative effects in the sizing and weaving process. High yarn hairiness causes mutual stickiness, higher yarn unevenness, higher abrasion and a greater number of yarn breaks on the loom . ShorterDesizing was carried out in two ways: by using ultrasound and washing off . HydrolyThe modification of corn starch was carried out with the aim of producing an environmentally friendly and effective sizing agent that works better than starch.Acrylic monomers were grafted onto the starch structure using the initiators AIBN, BP, and KPS.The results of yield, percentage, and efficiency of grafting, and the data on BP initiator indicated that the grafting reactions of AA and HEMA to starch were successful.FTIR analysis confirmed that these were new products of starch and vinyl monomers.Most monomers remained in the sample HS-AA-KPS, followed by the sample HS-HEMA-BP, with the fewest in the samples HS-AA-BP and HS-HEMA-AIBN, which confirms a more successful graft polymerization in the presence of these initiators.HPLC chromatograms  of aqueous extracts of synthesized starch copolymer samples (AA and HEMA) showed that, depending on the type of initiator used, AA BP has the highest peak height and the largest area under the diagram for monomers grafted with the initiator, while HEMA monomer grafted with the AIBIN initiator has the highest peak height and the KPS initiator has the largest surface area.The highest uniformity of molar mass was shown in samples of hydrolysed grafted starch, during an elution volume of 2.15–4.0 mL. The smaller molar masses of the grafted samples with an elution volume of 4.2–6.5 mL resulted in poorer homogeneity.The viscosity decreased with decreasing starch concentration. All grafted hydrolysed starches increased viscosity compared to non-grafted hydrolysed starches, indicating good stability of the potential starch.After impregnation of the yarn in sizing, the yarn mass yarn increased by the amount of the starch applied. Coarser single yarn as well as coarser plied yarn adsorbed or bound more starch, which is associated with a larger volume and more loose structure.The sizing process caused an increase in the breaking force. Before grafting, hydrolysed starch had a lower breaking force than grafted starch. The higher starch concentration had a higher breaking force. Starches with HEMA monomer gave better results than AA monomer in terms of breaking force of the yarn, which confirms their more homogenous distribution and good adhesion both on the surface and inside the yarn.Sizing reduced elongation at break of yarns and starches with HEMA monomer reduced elongation at break the least.Grafted starch proved to be a good agent for abrasion resistance, especially HS-HEMA, which can be ascribed to its good hydrophobicity, thus providing greater surface protection of the yarn. By the hydrolysis of corn starch and subsequent grafting, the yarn hairiness was significantly reduced in all yarns. An increase in the amount of starch caused less hairiness. Higher starch concentration had a better effect, as the number of fibres protruding in the direction of the measuring zones decreased considerably, especially in single yarns.Desizing of yarn using ultrasound gave better results than desizing by washing, even at lower size concentrations.Optical microscopy of the starch solution showed partially altered granules at different stages of swelling. Longer dormant starch state caused changes on the surface of acid hydrolysed starch granule, the granule surface became less smooth and the size increased.Tegewa numbers six and above generally occurred in all grafted starches, meaning that the desizing process was successful.On the basis of the analyses carried out, it can be concluded that there is an economic, qualitative, and ecological cost-effectiveness of the return of corn starch to the sizing process, but only by synthesizing and grafting with appropriate initiators, which significantly improves the properties.The following conclusions can be drawn from this research:


Many tumor cell types overexpress integrins, a glycoprotein, on their cell membranes. The tripeptide motif Arg-Gly-Asp (RGD) is well-known for being recognized by the integrin superfamily members and can thus be used to actively target nanoparticles containing cytotoxic drugs directly to the tumor cells. According to this strategy, the antitumor activity is boosted, and healthy organs are spared. In this paper, silk fibroin, a naturally derived protein, has been used to prepare nanoparticles (SFNs) functionalized on their surface with RGD. In vitro experiments revealed that functionalization of SFNs with RGD provided active internalization by tumor cells overexpressing integrin receptors. Therefore, RGD-SFNs may be used for tumor-specific delivery of anticancer drugs.Arg-Gly-Asp (RGD)-based cyclopentapeptides (cRGDs) have a high affinity towards integrin αvβ3 and αvβ5, which are overexpressed by many tumor cells. Here, curcumin-loaded silk fibroin nanoparticles (SFNs) have been functionalized on the surface with cRGD to provide active targeting towards tumor cells; a “click reaction” between the RGD-based cyclopentapeptide carrying an azide group and triple-bond-functionalized nanoparticles has been exploited. Both naked and functionalized SFNs were less than 200 nm in diameter and showed a round-shaped morphology but, after functionalization, SFNs increased in size and protein molecular weight. The functionalization of SFNs’ surfaces with cRGD provided active internalization by cells overexpressing integrin receptors. At the lowest concentration tested (0.01 mg/mL), functionalized SFNs showed more effective uptake with respect to the naked by tumor cells that overexpress integrin receptors (but not for non-overexpressing ones). In contrast, at higher concentrations, the non-specific cell membrane protein–particle interactions are promoted and coupled to specific and target mediated uptake. Visual observations by fluorescence microscopy suggested that SFNs bind to integrin receptors on the cell surface and are then internalized by endocytosis. Overall, SFN functionalization provided in vitro active targeting for site-specific delivery of anticancer drugs, boosting activity and sparing healthy organs. Cancer is one of the major disease burdens worldwide. Among the primary cancer treatment modalities, chemotherapy has been widely performed in the clinic because of its convenient and straightforward process  and stilAmong current drug delivery systems, nanoparticles have shown great potential in recent years ,5,6. SilInterestingly, the nanoparticle accumulation into the tumor can be increased by adopting active targeting strategies. An actively targeted nanoparticle is usually obtained by adding ligands’ surfaces for recognition by specific receptors/antigens on target cells . In thisThe coating of nanoparticles with integrin ligands has been explored to guide cytotoxic reagents directly to the cancer cell surface ,18. In tGiven these premises, this study aims to fabricate curcumin-loaded SF nanoparticles (SFNs), conjugated with cRGDs, to achieve active tumor targeting towards various cancer cell lines. Curcumin is here selected as a drug model and for its anticancer effects . In the ® Ultra filters were purchased from Sigma-Aldrich . Dialysis cellulose tubes were purchased from Visking, Medicell Membranes Ltd. . Moreover, 70 μm nylon meshes were purchased from Greiner Bio-One GmbH . Natriumazide and sodium sulphate were from Carlo Erba Reagenti . Caucasian colorectal adenocarcinoma cells (Caco-2), human cervix cancer cells (HeLa) and human urinary bladder (ECV) cancer cells were purchased from the European Collection of Authenticated Cell Cultures Cell Bank . All reagents used for cell cultures were purchased from Euroclone .Acetone, Azide-fluor 545, collagenase IA, curcumin, dimethylsulfoxide (DMSO), glutaraldehyde, ethanol, lithium bromide, methanol, potassium chloride, potassium dihydrogen phosphate, sodium carbonate, sodium hydroxide, 3--2,5-diphenyl-tetrazolium bromide (MTT) and Millipore’s AmiconBombyx mori cocoons according to previously reported procedures [2CO3) for 30 min. Then, the degummed fibers were washed in distilled water (37 °C) and dried at room temperature. A 9.3-M LiBr aqueous solution was prepared and used to dissolve SF fibers at 60 °C for 4 h. The obtained solution was placed into dialysis cellulose tubes  and dialyzed against distilled water at room temperature for 72 h. The SF final concentration was 8.16% w/v and was determined by freeze-drying known SF volumes  at −50 °C, 8 × 10−1 mbar for 72 h.SF was extracted by ocedures ,28. Briew/v and then added dropwise to the acetone, where curcumin was previously solubilized at a concentration of 0.08 mg/mL. SFN suspension was dialyzed against distilled water at room temperature for 72 h using dialysis cellulose tubes (12 kDa MWCO), freeze-dried at 8 × 10−1 mbar and −50 °C and stored at room temperature until use (maximum 2 months).SF nanoparticles (SFNs) were prepared by a desolvation method according to the procedures previously reported by our group ,9. SF aqBefore functionalizing SFNs with RDG, we performed bioconjugation with a fluorescent compound named Azide-fluor 545 (Molecular Weight 631.70 g/mol) . Azide-fg for 10 min, and supernatants were analyzed. A calibration curve (correlation coefficient R2 > 0.9899) was obtained to measure the Azide-fluor concentration; we consider the Azide-fluor concentration range of 0–10 µg/mL (deionized water was considered as control solution). Each measurement was performed in triplicate.The quantification of Azide-fluor conjugated on SFNs was evaluated with spectrophotometric analysis  at 554 nm. First, 2 mg of SFNs was suspended in 300 µL of distilled water, maintaining magnetic stirring overnight. After incubation, nanoparticles were centrifuged at 3250× 3 group. The key step, i.e., the Huisgen cycloaddition between FNPs and the azide-functionalized cRGD, was carried out in phosphate buffer in the presence of CuSO4 and sodium l-ascorbate. The final dialysis (cut-off 3–5 kDa MWCO) of the reaction mixture allowed the obtainment of pure cRGD-SFNs.The synthesis of cRGD-functionalized SFNs (cRGD-SFNs) was carried out by exploiting a “click reaction” between the azide group of the RGD-based cyclopentapeptide and a triple bond on the surface of SFNs . SFN funBoth nude and functionalized SFNs were characterized as follows.SFN production yield (Y%) was calculated as follows:v/v ethanol (0.1 mg/mL), maintaining mild magnetic stirring in the dark, and the absorbance was measured at 254 nm by a spectrometer . Ethanol was considered as blank. To extrapolate the drug content, a calibration curve was prepared using curcumin in the concentration range 0.25–10.00 μg/mL; R2 was 0.9957. The drug loading (% w/w) was calculated, dividing the total drug content  and the concentration of analyzed SFNs. All experiments were performed in triplicate.The amount of curcumin loaded into SFNs was quantified by spectrophotometric analysis. Briefly, SFNs were dissolved in 96% The encapsulation efficiency (EE%) was calculated as the percentage ratio between the drug entrapped in SFNs and the drug dissolved in the acetone solution.Particle size and size distribution of both naked and functionalized SFNs were measured by Nanoparticle Tracking Analysis . The instrument was fitted with a flow-cell top plate and a 405 nm laser. The temperature was set at 25 °C and the detection angle at 90°. Before carrying out NTA analyses, SFNs were dispersed in water, vortexed and sonicated for 15 min. Measurements were repeated 3 times for each sample, and results were analyzed with the NTA software 3.0.The polydispersity index (PDI) and zeta potential of both naked and functionalized SFNs were measured using ZetasizerNano ZS . Aqueous suspensions (1 mg/mL) of SFNs were prepared and allowed to equilibrate overnight at room temperature with gentle stirring. Then, the nanoparticle dispersions were filtered with a 0.45 μm filter and analyzed. The measurements were performed in triplicate for each sample. To define the Z-potential of the nanoparticles, 1 mM KCl was added to the aqueous suspension of 1 mg/mL.Morphology of both naked and functionalized SFNs was evaluated using SEM . Before the analysis, freeze-dried samples were gold-sputter-coated under argon.g and 4 °C using Millipore’s Amicon® Ultra Filters  with a Nominal Molecular Weight Limit (NMWL) of 10 kDa and load capacity of 500 µL. Deionized water was used as a washing solution. The collected samples were injected into the HPLC system. The instrument was an Agilent HPLC series 1100 system , equipped with a quaternary pump, an autosampler, a mobile phase online degasser, a thermostated column compartment and a diode array detector. The analytical column was a TSKgel SuperSW3000 (4.6 × 300 mm). SEC analysis was performed according to a previously reported method [2SO4 and 0.05% (w/v) NaN3 in 0.1 M phosphate buffer, pH 6.7. The elution was performed in isocratic conditions at the constant flow of 350 μL/min. The column temperature was maintained at 25 °C, and the injection volume was set at 5 μL. UV absorption was monitored at 280 nm. Calibration was performed using protein standards  at 60 °C for 4 h. The solution obtained was ultrafiltered 2 times (10 min each) at 10,000× d method . The mobards see . Analysev/v) FBS, 1% (v/v) penicillin/streptomycin and 1% (v/v) amphotericin B. MSCs fulfilled adherence to the International Society for Cellular Therapy criteria [Mesenchymal stem cells (AD-MSCs) were isolated from adipose tissue samples collected from patients undergoing abdominoplasty surgery after informed consent was obtained  and according to previously reported procedures ,31,32. Acriteria .Human fibroblasts (HF) were obtained from informed donors subjected to skin biopsy. Skin samples were digested as previously reported . Obtaine2 in DMEM-HG supplemented with 10% fetal bovine serum, non-essential amino acids (NEAA) 100×, penicillin 100 U/mL, streptomycin 100 μg/mL, amphotericin 0.25 μg/mL, glutamine 4 mM, sodium pyruvate 1 mM.Caco-2 cells were cultured at 37 °C and 5% COv/v) FBS, 1 mM glutamax, 1% v/v antibiotics (penicillin-streptomycin) and 1 mM pyruvate at 37 °C, under a humidified atmosphere containing 5% CO2.HeLa were cultured in DMEM with a low content of glucose (1 g/L), supplemented with 10%  and cultured with their culture media as described in sample is the mean value of the measured absorbance of the tested samples, and Absctr is the mean value of the measured absorbance of cells not incubated with SFNs. All experiments were performed in triplicate.The cytocompatibility of both naked and functionalized SFNs was evaluated by the MTT test on all the cell lines reported in 2. After 24 h of incubation with culture medium  glutaraldehyde solution in PBS for 3 h at 4 °C and washed four times with PBS. Naked and functionalized nanoparticles taken up by fibroblasts ECV and Caco-2 cells were visualized under a Zeiss Axioskop 40 microscope  equipped with a 40 × 0.75 objective lens and an RT Slider camera .The experiments were repeated on Caco-2 and ECV cells at 60, 180 and 360 min. These two cell lines display opposite integrin subunit expression patterns: Caco-2 cells express very low integrin subunit mRNA levels, particularly β3, while in ECV, integrin mRNA levels appear to be higher, and β3 is very abundant see . TherefoThe microscopy fluorescence images acquired were firstly pre-processed using ImageJ  and thenp < 0.05. Unless otherwise specified, data are expressed as mean ± standard deviation.Raw data were processed by STATGRAPHICS XVII . For data with a normal distribution, a linear generalized analysis of variance model (ANOVA) was used and combined with Fisher’s least significant difference (LSD) procedure to evaluate the differences between the groups. For all the analyses, the statistical significance was set at w/w), with an encapsulation efficiency of 83.58%. These results agree with our previous works [w/w. The alkyne linker, consequently the Azide-fluor, selectively reacted and attached the Lysine residues on SFNs’ surfaces with a 1:1 stoichiometric ratio reaction. Starting from this assumption, we considered the molecular weight of Azide-fluor (631.70 g/mol) to obtain the bioconjugation data expressed as 3.64 nmol of reacted Lysine for mg of SFNs.SFNs were prepared by a desolvation method. The addition of acetone as a desolvating agent reduces fibroin chains’ hydration until fibroin protein precipitates in the form of nanoparticles . After fus works ,38, thusp < 0.05). Naked SFNs showed a mean diameter of 128.9 ± 2.4 nm, and the d10, d50 and d90 were 84.9 ± 0.8, 109.8 ± 0.9 and 201.5 ± 12.6 nm, respectively . For cRGD-functionalized SFNs, the mean diameter was 142.7 ± 2.7 and the d10, d50 and d90 were 96.7 ± 1.8, 129.1 ± 2.8 and 205.0 ± 3.3 nm, respectively   A,B. Part, n = 3) C. LargerAnalytical size exclusion chromatography (SEC) was selected to compare the elution profiles of naked and functionalized SFNs due to its ability to elute analytes in order of their molecular size. The SEC profile of solubilized naked SFNs A revealsp > 0.05, see Drug release studies have been performed on both naked and functionalized SFNs, as reported in the Before starting treatments with naked and functionalized nanoparticles, the cells used in this study were tested for RGD-binding integrin mRNA expression by real-time qRT-PCR, as described in the p < 0.05), and especially on the Caco-2 cell line, where the cell metabolic activity was reduced to 27.9 ± 6.594 already at the lowest concentration considered (0.01 mg/mL). No dose-dependent effect was observed (p = 0.06). It is not clear what caused the apparent decrease in the viability for functionalized nanoparticles at concentrations above 0.01 mg/mL, but since there is no dose-dependent continuous decrease, it is hard to say that the nanoparticles caused severe cytotoxicity [toxicity .p < 0.001); at the high concentrations tested , no significant differences were observed among the uptake of functionalized or naked SFNs by all the cell lines considered. However, at the lowest concentration tested (0.01 mg/mL), functionalized SFNs were more effectively taken up by ECV cells, which overexpress integrin receptors  was further confirmed by microscopy (exploiting the fluorescence of fibroin and curcumin) using Caco-2 (which do not overexpress integrin receptors) and ECV (which overexpress integrin receptors). For Caco-2 cells, no different behavior was revealed among naked and functionalized SFNs at 1 and 3 h. Only after 6 h of incubation, a slight internalization of functionalized SFNs is detectable as an increase in fluorescence in the vicinity of the cell membrane (p < 0.001). For Caco-2 cells, fluorescence intensity was not significantly influenced by the functionalization (p > 0.05); for ECV cells, the treatment time was significant (p = 0.0495), and an increasing trend was detectable. These results confirm what was observed visually and support the supposed uptake mechanism.To further confirm what was observed, the images acquired were processed to extract the average intensity values of fluorescence. ECV cells fluoresce significantly more than Caco-2 cells (lization A. For EClization B. For CaCurcumin-loaded SFNs were prepared by a desolvation method and then functionalized with cRGD to provide active targeting towards tumor cells that overexpress integrin receptors. A “click reaction” was exploited between the RGD-based cyclopentapeptide carrying an azide group and triple-bond-functionalized nanoparticles. SFNs showed round-shaped morphology, and the mean diameter was 128.9 ± 2.4 and 142.7 ± 2.7 for naked and functionalized SFNs, respectively. After functionalization, a higher-MW protein population was observed by comparing the SEC elution profiles, suggesting proper functionalization. The functionalization of SFNs’ surfaces with cRGD provided active internalization by cells overexpressing integrin receptors, such as ECV. In detail, a marked uptake for functionalized SFNs was observed for ECV cells already after 1 h. In contrast, for Caco-2 cells, which do not overexpress integrin receptors, no differences were revealed between naked and functionalized SFN uptake at 1 and 3 h. Only after 6 h of incubation, a slight internalization of functionalized SFNs is detectable as an increase in fluorescence in the vicinity of the cell membrane. Overall, SFN functionalization provided in vitro active targeting for site-specific delivery of anticancer drugs.