Typically, we observed transient domains of both chiralities, separated spatially from each other by domain walls with different structure. In addition, we observe transient density of states modulations consistent with interference of L and R-handed charge density waves within the surface monolayer. Theoretical modeling of the intertwined domain structures using a classical charged lattice gas model reproduces the experimental domain wall structures. The superposition (S) state cannot be understood classically within the correlated electron model but is found to be consistent with interferences of L and R-handed charge-density waves within domains, confined by surrounding domain walls, vividly revealing an interference of Fermi electrons with opposite chirality, which is not a result of inter-layer interference, but due to the interaction between electrons within a single layer, confined by domain wall boundaries.Mirror symmetry plays a major role in determining the properties of matter and is of particular interest in condensed many-body systems undergoing symmetry breaking transitions under non-equilibrium conditions. Typically, in the aftermath of such transitions, one of the two possible broken symmetry states is emergent. However, synthetic systems and those formed under non-equilibrium conditions may exhibit metastable states comprising of both left (L) and right (R) handed symmetry. Here we explore the formation of chiral charge-density wave (CDW) domains after a laser quench in 1T-TaS Some of these superlattices break crystal mirror symmetry, which occurs when the superlattice ordering vector is not aligned with a symmetry axis of the atomic lattice. Such superlattices can exist in two possible chiralities, and we can transform one into the other by a mirroring operation over a high symmetry axis of the atomic lattice. If we write the superlattice unit vector as a combination of the in-plane atomic unit cell vectors 1, and appears in various materials, including 1T-TaS2, 2Hb-TaS2, 1T-TaSe2 and 2Hb-TaSe22. As a special case, also the 23. Energetically, the L and R-handed superlattices are equivalent4. A mixture of the two would result in domain walls between them, which is energetically costly6 and thus coexisting mirrored domains are experimentally rarely found under equilibrium conditions. The presence of mirrored domains was nevertheless observed in the scattering experiments7, but it was not investigated in detail until recently10. The scattering experiments are in this case limiting, as they simultaneously probe many layers as well as a relatively large area within each layer, and thus give little or no information on the microscopic ordering, making it unclear whether the L and R domains exist within a single layer or across many layers. Recently Ohta et al. investigated stacking of L and R domains in Nb substituted 1T-TaSe2, reporting different electronic states due to the different stackings11.The hexagonal atomic lattice, which is common in layered 2D materials, supports commensurate (C) electronic superlattice ordering with various sizes of unit cell. Experimentally, the size of the superlattice unit cell has been observed in the range between 3 to 16 lattice constants, and values in between, which are allowed by the geometrical cosine rule2 leads to the appearance of the symmetrically equivalent CDW diffraction peaks which were attributed to the mirrored superlattice orientations12, whereby the probability of switching increases with increasing the laser fluence. After the excitation, both diffracted peaks were present in regions of the size of 1.1 μm. Due to the experimental limitations, it was not clear whether this is an interlayer or an intralayer effect, and how the domains order and interact. In addition to mixed L and R superlattice states, an intriguing possibility exists in quantum systems. Considering that L and R configurational states are energetically degenerate, a superposition (S) of the L and R state is also possible. While CDWs are commonly described as classical objects, in which superpositions can occur, properties such as CDW tunneling reveal their quantum nature15. In the quantum description, the CDW can be thought of in terms of a standing wave, arising from an interference of counter-propagating electrons with wavevector In non-equilibrium systems, however, various metastable states may be observable. It was recently shown by Zong et al. that applying an ultrafast laser pulse to a thin flake of 1T-TaS2 created by laser excitation in the low-temperature C state. The STM images show the local density of states (LDOS), which in the quasiparticle approximation is given by: 11, and for confined electron trajectories in transition metal dichalcogenide heterostructures12. The observations by STM are classical, but the observed quasiparticle interference phenomenon is treated by solving the Schrödinger equation for counterpropagating quasiparticles. Since the observed order parameter does not have any out-of-plane component (STM scans are 2D and surface sensitive), we primarily consider the system as two-dimensional, where CDWs tilted L and R with respect to an in-plane crystal axis are considered two different chiralities.Using scanning tunneling microscopy, we investigate the microscopic structure of the mirror domains in the surface layer of 1T-TaS2 is a quasi-two-dimensional transition metal dichalcogenide, where tantalum atoms are sandwiched between two layers of Sulphur atoms  CDW state occurs at 350 K, where the direction of the charge modulation is misaligned with the lattice by +17. Below 180 K, the CDW becomes commensurate (C) and insulating18. Here, the angle between the 4. The superlattice unit cell is formed with 13 atoms, where twelve of the atoms move towards the thirteenth central atom to form a David-star-like cluster, as shown in Fig. 22. STM studies of the surface show that the uniform CDW pattern is broken into smaller domains. The domains and domain walls are metastable at low temperatures, which allows us to investigate their non-periodic microscopic order by STM22. The H state formation is macroscopically a very reproducible phenomenon, as shown by electrical and optical experiments24, but the microscopic domain distribution appears to be different after each switching attempt24, which is in line with the probabilistic nature of the appearance of the mirror domains at higher temperatures12. X-ray and electron diffraction experiments26 show that interlayer stacking plays a role in ordering within the H state, but do not reveal any domain structure. STM observations on the other hand reveal that long-range order of the surface layers is broken in the H state. With STM we only probe the top layer and thus observe only the ordering along the h and k axis , while it is not possible to probe the out-of-plane dimension and thus hard to reach conclusions about the bulk. An important thing to note is that in three dimensions, the CDW state can have 4 possible orientations, as in addition to the symmetry within the h–k plane, we must also consider the mirroring over the h–k plane, thus negating the l component of the CDW. Since the observed order parameter does not have any out-of-plane component, we can distinguish only the difference within the h–k plane, while the symmetric orderings with respect to the l direction appear identical. In this sense we consider the system as two-dimensional, justifying the use of the term chirality to describe L and R domains.1T-TaSApart from finding a rich variety of domain walls between L and R domains, that are not observed in equilibrium crystals, we also observe metastable domains where the local density of states shows complex flower-shaped spatial patterns, in which twofold symmetry axis is restored. We show that the symmetry and observed patterns can be understood in terms of superpositions of L and R states. We successfully model the domain walls using a charged lattice gas (CLG) model, while the complex interference patterns are modelled in terms of superpositions of L and R CDWs.24. The switching laser fluence of about 3–5 mJ/cm2 is sufficient to form a number of such domains, which are sometimes intermixed with regions of an amorphous electronic phase27. The mirrored domains appear either alone, or in groups. Unfortunately, it is hard to estimate their density from present STM experiments, because relatively small areas are probed. A typical boundary between two different domains is shown in a large area image in Fig. 28 in large area scans, and—as we shall see later—also in model simulations29, the domain walls between L and R domains tend to be ragged, and their width is not easily defined. We have found that similar, mirrored domains can also be induced by a current pulse from the STM tip, but this method of excitation is not very uniform, and the result is local and not very reproducible.To induce the formation of mirrored domains, we perform a laser quench using a single or multiple 50 fs near-infrared (800 nm) laser pulses to drive the sample inside the STM chamber out of equilibrium Fig. d. After entclass1pt{minimaentclass1pt{minimaApart from neighboring L and R-handed domains, we also observe domains containing characteristic ‘flower-shaped’ interference patterns Fig. d, e, whientclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minima2. Here the top layer has the same 1T polytype structure as 1T-TaS2, but the second layer has a 1H polytype structure, so its S pattern cannot be the result of interference between the first two layers.  In equilibrium samples without domains  the S pattern is conspicuously absent when the first and second layers have opposite chirality. , the domain walls of the second layer are faintly discernible, yet the CDW pattern within the top layer domains does not show any significant change of the LDOS modulation due to the phase-shifted layer underneath1 in the Wigner crystal limit. The use of this model is justified by its success in describing the phase diagram of the material, particularly the commensurate phases at different fillings, the domain structure, and particularly, the presence of an amorphous phase24. The filling 1. Figure In order to obtain insight into ordering of the mirrored domains, we first compare the measurements to the results of Monte-Carlo calculations of sparsely filled, screened, correlated electrons within a charge lattice gas (CLG) model on a hexagonal latticeOur experiments show that domains with different chiralities can be reached through processes in which the relaxation path goes through an intermediate state with restored mirror symmetry Fig. c, d. Whe27. The most commonly observed color (light green) corresponds to the superlattice unit cell of the commensurate CDW. In the model, the domains are homogeneously green, while in the experimental image occasional deviations are seen due to measurement errors. In the domain walls the polarons can be either more closely or more sparsely packed, which is evident from the coloring.Colored tiling performed with diamond shapes  pair therefore adds a wedge and removes another wedge, leaving the material with an additional semi-infinite stripe of unit cells32. H–P pairs in the domain wall crossings between domains of the same type thus add a nonzero-thickness stripe of material, which is the domain wall itself. A H–P pair is topologically equivalent to a crystal dislocation on a hexagonal lattice. In this sense, both free standing pentagons and heptagons, as well as their pairs are topologically protected. On the other hand, the domain walls between domains of different directions are composed of a series of such H–P pairs. In analogy to graphene, a series of such pairs leads to a nonzero angle between the neighboring lattices32, which is equivalent to the case that we discuss here. Additionally, since the H–P pairs highlight the domain walls very well, we can use them as a guide to determine the domain wall directions. In Fig. To examine more closely the ordering within the domain walls we determine the number of nearest neighbors of each polaron by constructing a Voronoi diagram Fig. c, g. Wit2 FS nesting was suggested to contribute to the CDW instability16. Irrespective of the extent of such nesting, we may consider a picture of the CDW, in which FS electrons form interference patterns of L and R-handed superstructures. The H state is metallic, and the system has a Fermi surface, so we may discuss the system behavior in terms of the quasiparticle picture. Starting from a Schrödinger equation description of the CDW14, with degenerate L and R solutions for the broken symmetry ground state, a linear combination of states describes the superposition. This is true irrespective of the detailed interaction Hamiltonian, but requires the assumption that the state can be described by a Schrödinger Hamiltonian14. The L and R CDWs can thus be described in terms of the sum of one-directional CDWs:While the mixed L/R domain state can be described by the CLG model quite well, to describe the observed interference, we need to go beyond the strongly correlated classical polaron model. While Fermi surface (FS) nesting is considered to be rarely responsible for CDW formation in 2-dimensional materials, 1T-TaS16: In the high-temperature IC state, the CDW is aligned with the lattice . The predicted single chirality displacements are shown in Fig. It is interesting to consider the role of the atomic displacements in the superposition state. In this material, a Kohn anomaly is observed, associated with the IC transition, indicating that mentclass2pt{minim2 layers are considered.A conceptual free energy diagram is shown in Fig. intra-layer interference in the context of commonly observed multi-layer interferences (Moiré patterns), such as previously observed on the surface layer of Nb-substituted 1T-TaSe2 by Ohta et al.8. In the latter case the observed modulation arises from the interaction of the two topmost layers with different 2D chiralities. In the present case, we have argued in the results section that the layer below is not directly responsible for the L + R interference, and is fundamentally different from such inter-layer Moire patterns. The observation of an intra-layer interference appears as a manifestation of the quantum behavior of the CDW for electrons confined within a domain created during the quench process. We note that a related effect of intra-layer quantum interference arising from in-plane electron confinement within triangular heterostructures was recently reported, although only irregular interference patterns were observed28. In principle, the L + R interference effect within domains is possible for all CDW superlattices that have broken in-plane mirror symmetry with respect to the crystal lattice  enabling fast scanning of metastable domains. The tip currents were kept below 1 nA to avoid influencing the dynamics as much as possible. The usual time between the optical excitation and the STM scanning varies between minutes to hours, mainly depending on the time needed to find a suitable area that exhibits interferences.For the STM measurements we use a UHV LT Nanoprobe (Scienta Omicron) with optical access through obliquely angled side windows. For the photoexcitation, we use a 100 kHz, 800 nm laser system, with 50 fs pulses. The number of pulses was selected using an acousto-optic modulator. The laser beam is guided into the STM chamber using an automatic stabilizing system with a positioning precision of 27 for details) in the Wigner crystal limit. 1, where we studied the phase diagram of such a system at fixed values of The model of classical chiral domains is based on the charged lattice gas (CLG) Hamiltonian qualitatively the same result for We use the Lennard–Jones equation Supplementary Information.


The accuracy of the constitutive model was verified through numerical simulation of 2195 Al-Li alloy extruded profiles with large shaped cross-sections. Dynamic recrystallization occurred at different regions during the practical extrusion process, resulting in slight variations in the microstructure. The differences in microstructure were due to the varying degrees of temperature and stress experienced by the material in different regions.The quality of extruded profiles depends largely on accurate constitutive models and thermal processing maps. In this study, a modified Arrhenius constitutive model for homogenized 2195 Al-Li alloy with multi-parameter co-compensation was developed and further enhanced the prediction accuracy of flow stresses. Through the processing map and microstructure characterization, the 2195 Al-Li alloy could be deformed optimally at the temperature range of 710~783 K and strain rate of 0.001~0.12 s Compared with ordinary aluminum alloys, Al-Li alloy components possess lighter weight, higher mechanical properties and fatigue resistance ,2. TheseThe accuracy of extrusion numerical simulation and the consistency of profiles depend heavily on an accurate constitutive model. Consequently, different types of constitutive models have been developed and have gained some applications. Jonas et al.  first es1 phase. Wang et al. [−1 and the material undergoes deformation instability. During thermal deformation, alloys with the same composition in various states will exhibit considerably variable power dissipation efficiencies. Therefore, it is necessary to study the effect of alloy state on the evolution of microstructure.The work hardening and dynamic softening coincide in the high-temperature rheological process of aluminum alloy, where dynamic recovery (DRV) and dynamic recrystallization (DRX) are the main softening mechanisms. The microstructure of alloys is usually affected by the thermal deformation parameters, and the specific microstructure formed after deformation is the main factor leading to the difference in material properties. The processing map based on the dynamic materials model (DMM) proposed by Prasad et al.  can reflg et al.  discoverCurrently, significant progress has been made in researching the hot deformation behavior of aluminum alloys. However, there are few successful cases where the obtained constitutive model and hot processing map have been applied to actual industrial production, particularly for Al-Li alloys. Dong et al.  simulate−1, a 60% height depression, and a deformation temperature range of 643–693 K. The specimen was first heated to the required temperature at a rate of 5 K/s, held there for 3 min during the test, and then hot-compressed at a specific strain rate. Finally, water-cooled quenching was applied immediately after reaching the required reduction to preserve the high-temperature microstructure. Before the hot compression experimental process, graphite foils were placed between the upper and lower ends of the specimen and the contact surface of the WC anvil to reduce friction.The 2195 Al-Li Alloy was provided by Southwest Aluminum (Group) Corporation of China Ltd. , and the chemical composition of the alloy is 3.98Cu, 0.99Li, 0.32Mg, 0.32Ag, 0.12Zr, 0.08Fe, 0.04Si (wt%) and a balance of Al. The material was sampled at the center of the ingot after a two-stage homogenization treatment of 470 °C/7 h + 525 °C/24 h and machined into a hot compression specimen of Ø8 × 12 mm for diameter and height. Hot compression tests were performed on the Gleeble-3500D thermomechanical simulator with a strain rate range of 0.001–1 s2H5OH + 10% HClO4) for 5–8 s at room temperature using the parameter of voltage 20 V. The collected EBSD data were analyzed and processed using HKL Channel-5 software.The as-cast and homogenized microstructures were observed by metallographic microscope (OLYMPOS-DSX500) and scanning electron microscope , respectively, and the chemical composition of the second phase was analyzed by energy dispersive spectrometer . In addition, the composition and type of phases contained in the two alloys were identified by X-ray diffractometry (D8 Advance). The microstructural characterization of hot-compressed samples with different process parameters and profiles in different regions after the actual engineering extrusion was carried out using electron backscatter diffraction (EBSD) to investigate the deformation mechanism behind them, which was performed at the Helios Nanolab 600i electron microscope. The sampling position of the hot compressed samples was located in the central area along the compression axis, and the profile was divided into three regions: P1, P2 and P3. The practical 2195 Al-Li alloy extruded profile is shown in 2Cu phase, while the skeleton second phase is primarily made up of Al, Cu, and Fe elements. Following homogenization, as seen in 7Cu2Fe phases. Based on the results of the XRD analysis of the as-cast and homogenized states shown in 1(Al2CuLi), T2(Al6CuLi3) and S(Al2CuMg) phases. However, after homogenization, these phases are essentially redissolved into the aluminum matrix.The OM, SEM and XRD diagrams of the as-cast and homogenized 2195 Al-Li alloy are shown in The true stress-strain curves of the two-stage homogenized 2195 Al-Li alloy obtained by isothermal hot compression tests at different deformation conditions are shown in At the initial stage of deformation, the stress rises rapidly with the increase in strain, and then decreases gradually when the stress reaches the peak, and finally stabilizes. At the fixed deformation temperature, the stress rises with the increase in strain rate because the dislocations caused by the rapid deformation are not ready to eliminate and rearrange in a short time, which leads to an increase in the work hardening rate. Due to the thermal activation of metal atoms being strengthened at higher temperatures and the metal’s deformation resistance declining, the stress reduces with increasing deformation temperature at the same strain rate. Additionally, DRV and DRX tend to occur when the alloy is deformed at high temperatures, resulting in alloy softening ,22.−1), σ is the flow stress (MPa), R is the universal gas constant (8.314 J mol−1 K−1), T is the thermodynamic temperature (K), Q is the deformation thermal activation energy (kJ mol−1), and A, α, n1, n, and β are material constants, where α = β/n1. To calculate the value of each constant, Equation (2) is brought into Equation (1) on each side and the logarithm taken to obtain:The Arrhenius hyperbolic sinusoidal constitutive equation is typically used to depict the connection between flow stress, deformation temperature, and strain rate of metal or alloy during thermal deformation, that is:n1 and β can be regressed to 6.7498 and 0.1357 using the linear fitting method, respectively, then α = β/n1 = 0.0201.The solutions for each parameter in this experiment are used for peak stresses with different deformation conditions, and the specific data are shown in For all stress states, combining Equations (1) and (2), and taking partial derivatives on both sides gives:n = 4.9057. According to the obtained n and the average value of Q/nR obtained by linear fitting the data in Q can be calculated as 249.722 kJ mol−1. Based on obtaining n and Q, combined with A can be obtained as 2.5052 × 1016. Based on the fitted material parameters, the isothermal hot compression constitutive equation is obtained as shown in Equation (5).Based on the peak stress value, the functional relationship between Since the strain rate is controlled by the thermal activation energy and temperature during plastic deformation, this coupling relationship can be expressed by the Zener-Hollomon coefficient, which can be rewritten as:The expression for the flow stress containing the Zener-Hollomon coefficient can be obtained from the definition of the hyperbolic sine function as follows:The calculated data are brought to the hyperbolic sine function with the Zener-Hollomon coefficient at peak stress, which can be expressed as:The Arrhenius model previously established is a function of flow stress on deformation temperature and deformation rate, and does not consider the influence of deformation degree on flow stress. In order to more accurately predict the flow stresses in the alloy during the hot compression process, it is necessary to establish a strain-compensated Arrhenius constitutive model that considers the deformation temperature, deformation rate and deformation degree simultaneously.α, n, Q, and lnA at different strains . In this experiment, as shown in Equation (9), a fifth-order polynomial function [α, n, Q, and lnA are shown in The linear regression method can be used to find the values of material parameters such as function ,16 is usThe Arrhenius constitutive model of the homogenized 2195 Al-Li alloy considering strain compensation obtained by polynomial fitting of the material parameters can be expressed by Equation (9), which can be used to predict the flow stress for any given deformation condition.To investigate whether the established Arrhenius equation is consistent with the actual flow behavior of 2195 Al-Li alloy at different deformation temperatures and deformation rates, the flow stress values calculated by Equation (10) were compared with those obtained from actual hot compression tests, and the results are shown in −1) and deformation temperatures of 643–693 K. The predicted value is only 85.1% of the actual value, especially when the strain rate is 1 s−1 and the deformation temperature is 643 K. This implies that the flow stress behavior of 2195 Al-Li alloy cannot be well described by strain compensation correction alone.At high temperatures and low strain rates, the strain-compensated Arrhenius constitutive model fits the actual stress-strain curve more accurately, as seen in The difference between the predicted and test stress values is quantified using the related coefficient (R) and average absolute relative error (AARE), which can be calculated using Equation (11) and Equation (12), respectively. R and AARE have computed values of 0.9758 and 9.51%, respectively. To further correct the Arrhenius constitutive model with strain compensation described previously, it is required to take into account the compensation of the flow stress by strain rate and deformation temperature.In this section, based on the already established Arrhenius constitutive equation considering strain compensation, a modified function for deformation temperature and strain rate is introduced, to establish an integrated constitutive model considering strain rate, deformation temperature and strain co-compensation, as shown in Equation (13). As indicated in After calculation, the values of R and AARE are 0.9974 and 6.49%, respectively, which are significantly more accurate than the previous model. Therefore, the strain-compensated Arrhenius constitutive model considering strain rate and temperature corrections can accurately describe the flow behavior of 2195 Al-Li alloy.P can be split into two parts: content G and co-content J. The strain rate sensitivity coefficient m can be used to express the relationship between temperature and strain rate under constant temperature and strain combinations.The processing map based on DMM, which comprises a power dissipation efficiency map and an instability map, and contains two portions of the safety domain and instability domain, can reflect the relationship between the microstructure evolution mechanism and the alloy’s thermal deformation parameters. During thermal deformation, the material can be regarded as an energy dissipater, and the total dissipated power m = 1, and J obtains the maximum value Jmax. For a nonlinear dissipater, the power dissipation efficiency η can be expressed as the ratio of J to Jmax as follows:For an ideal linear dissipater, η does not mean better workability of the alloy, because the value of η under the conditions corresponding to the workability instability domain may also be larger [However, a larger value of e larger ,24. There larger  is used ξ < 0, plastic flow destabilization will occur, that is, it is more likely to produce adiabatic shear bands, flow localizations and other microstructure defects during deformation.When η. It has been confirmed that the microstructure of the safety domains is mainly related to DRV, DRX and phase transition [η usually indicates more energy for microstructure evolution and better plastic deformation properties under the corresponding deformation conditions [η.The processing map of the homogenized 2195 Al-Li alloy during hot compression with a strain of 0.8 was plotted in ansition . The hignditions . In gene−1, and the other is in the high-temperature range of 743–793 K with a moderate strain rate of 0.01–0.1 s−1, as depicted in −1 and medium temperatures of 673–703 K. Simultaneously, three instability domains are evident in the low-temperature, low-strain-rate region , the low-temperature, high-strain-rate region , and the high-temperature, high-strain-rate region . The occurrence of the peak area of power dissipation at low temperature and low strain rate suggests the occurrence of DRV in the alloy. Meanwhile, the appearance of the peak area of power dissipation at high temperature and medium strain rate may be attributed to CDRX. Generally, alloys tend to undergo destabilization when deformed within the high-temperature and high-strain-rate range, consistent with the findings of Zhang et al. [−1, which requires verification through microstructural analysis.The power dissipation exhibits peak areas in two temperature ranges: one is in the low-temperature range of 673–693 K, where the strain rate is below 0.001 sg et al.  and Wangg et al. . However−1) and C  are stable and regions B  and D  are unstable. The microstructure of these four regions was tested to analyze and discuss the deformation mechanism under different deformation conditions.Therefore, four typical regions were selected in the processing map; regions A , with a significant difference in misorientation from the adjacent grains, indicates that DRX occurred under this condition [−1. It can be seen that the majority of the grains are distributed with uniform LAGBs inside, while only a small number of deformed grains with distinct grain boundary contours have almost no LAGBs inside. Moreover, adiabatic shear zones appear in specific locations (marked with yellow boxes). As observed in ondition , which iWhen the deformation condition is in the safety domain C, the power dissipation efficiency increases from 0.24 to 0.32. It can be seen from −1 (unstable zone B). Numerous dislocations accumulate at certain original HAGBs, forming a mass of dislocation walls and tangles. Conversely, there is no apparent presence of dislocations within another portion of the coarse grains, indicating the alloy’s instability under this deformation condition. Furthermore, the formation of DRX grain was observed near the original HAGB, which possess diameter larger than 2 μm. Additionally, a certain number of second phase particles exist at the grain boundaries, effectively pinning them and impeding dislocation movement. In the case of deformation occurring within the stable region C, as depicted in The effects of deformation process parameters on dislocations and substructures were investigated using TEM, and the results are presented in −1.Considering the established processing map and the detected microstructure, the optimum deformation parameters of the homogenized 2195 Al-Li alloy were finally identified as 710–783 K and 0.001–0.12 sThis section describes the flow behavior of the material during thermal deformation using the established constitutive model. The model is then applied to the finite element simulation of 2195 Al-Li alloy extruded profiles with large shaped cross-sections in HyperXtrude software, and the extrusion parameters are shown in The results of the numerical simulation are presented in −1 to 0.043 s−1. The range of value variation falls within the feasible region  of the processing map established in In summary, the deformation temperature of the alloy ranges from 745 K to 765 K, and the deformation rate ranges from 0.000034 sPractical extrusion tests were carried out on a 25 MN extruder to verify the accuracy of the constitutive model and numerical simulation, and the extruded profile of 2195 Al-Li alloy with high dimensional accuracy was successfully obtained, as shown in To investigate the microstructure evolution during extrusion, EBSD analysis was performed on three observed surfaces of the profile, as shown in Further investigation reveals the presence of smaller recrystallized grains exhibiting a chain distribution along the elongated grain boundary, with a small number of recrystallized grains also observed within the original grains, indicating that CDRX and DDRX occur concurrently during extrusion deformation. By utilizing the established multiparameter compensated constitutive model and processing map, the physical field distribution during the steady-state extrusion deformation stage of 2195 Al-Li alloy was accurately predicted. The microstructure analysis confirmed the production of high-quality extruded profiles. The successful fabrication of extruded profiles from 2195 Al-Li alloy serves as a compelling validation of the extensive applicability of accurate numerical simulations in industrial manufacturing. This approach not only reduces development costs and time but also enhances production efficiency and ensures stability in product quality.An Arrhenius constitutive model considering deformation temperature, strain rate and strain co-compensation was established based on the true stress-strain data of homogenized 2195 Al-Li alloy after friction and temperature correction. This model significantly improved the accuracy of flow stress prediction during hot compression, with R and AARE values increasing to 0.9974 and 6.49%, respectively;−1;The processing safety zone and instability zone of 2195 Al-Li alloy were identified by employing the hot processing map. During hot compression, the alloy experienced both DRV and DRX. In the instability zone, considerable local plastic deformation bands and abnormally grown recrystallized grains were observed. The optimal deformation parameters for the 2195 Al-Li alloy were determined as 710~783 K and 0.001~0.12 sThe physical field distribution of 2195 Al-Li alloy extruded profiles with large shaped cross-sections during extrusion was accurately predicted by a modified Arrhenius constitutive model. Practical extrusion tests produced extruded profiles with slight variations in microstructure in different regions. These variations were caused by uneven temperature and stress distributions, with higher temperature and more severe stress promoting the formation of HAGBs and DRX grains.In this study, the constitutive model and processing map of 2195 Al-Li alloy were established, and the accuracy of the constitutive model was proved by numerical simulation and practical extrusion test. The main conclusions are as follows:


Domains are functional and structural units of proteins that govern various biological functions performed by the proteins. Therefore, the characterization of domains in a protein can serve as a proper functional representation of proteins. Here, we employ a self-supervised protocol to derive functionally consistent representations for domains by learning domain-Gene Ontology (GO) co-occurrences and associations. The domain embeddings we constructed turned out to be effective in performing actual function prediction tasks. Extensive evaluations showed that protein representations using the domain embeddings are superior to those of large-scale protein language models in GO prediction tasks. Moreover, the new function prediction method built on the domain embeddings, named Domain-PFP, substantially outperformed the state-of-the-art function predictors. Additionally, Domain-PFP demonstrated competitive performance in the CAFA3 evaluation, achieving overall the best performance among the top teams that participated in the assessment. A self-supervised learning method to generate functionally informed embedding representations for protein domains, capable of performing protein function prediction with state-of-the-art accuracy. Although protein functions are eventually determined by experiments, the experimental effort and expense slow down the process of function discovery, which is in contrast to the ever-increasing volume of sequenced proteins2. At present, not even 1% of sequenced proteins have functional annotation3. Unlike relatively cheaper sequencing technologies, there is a deficit of scalable, high-throughput experimental assays to functionally annotate proteins4. This has led to the demand for in-silico methods of automated protein function prediction5. Protein functions have been determined naturally from sequence similarity to known proteins6 and other characteristics of proteins that can trace functional relevance. Such information includes structural configuration9, phylogenetic information11, domain distribution14, protein networks15, and combinations of multiple sources17. Recently, various deep learning-based methods were proposed to learn a functional representation of proteins22. Such methods demonstrated substantial improvement over traditional database search-based methods24.Protein function prediction is one of the long-standing, fundamental topics of bioinformatics, which involves profiling the activities and interactions of proteins25. Therefore, it is compelling to infer the functions of a protein based on the presence and distribution of the various domains in it. InterPro2GO is an ongoing project that assigns GO annotations to specific domains in the InterPro database, and this annotation is done manually by experts27. Although the domain-GO mapping by InterPro2GO provides curated information on protein function, the coverage is severely limited. For example, there are approximately 38k InterPro entries and 48k GO terms, but the current version of InterPro2GO (version-date: 2022/03/16) mapping only includes 16,443 unique InterPro entries and 6,482 GO terms. Despite the lack of annotations, several methods have tried to leverage protein domain information for function prediction. Messih et al. analyzed the recurrence and order of protein domains and their influence on protein functions13. Rojano et al. attempted to associate domains and functions through tripartite graphs14. Besides such domain-focused studies, protein domains have been consistently used as a source of complementary functional information in a number of ensemble methods17, and some analyses even revealed that domain information is the most crucial one16.Proteins consist of domains, which are functional and structural units responsible for specific functions and interactions22, a 26,406-dimensional input of InterPro feature vectors was reduced to 1024 dimensions using a single multi-layer perceptron (MLP) layer, which results in considerable information loss. A similar situation is observed in DeepGraphGO21 as well.As in many other areas in bioinformatics, deep learning has been applied for function prediction from domain information. However, the effective use of domains is critically constrained by low coverage of functional assignments, high dimensionality, and acute data imbalance. For instance, in a recent competitive deep-learning-based model, DeepGOZero28. We used self-supervised learning because it can directly learn domain and GO co-occurrence from abundant protein sequences and is able to alleviate the problem of current domain databases, where many domains do not have function annotation. Following the underlying concepts of self-supervised learning, we first learned pseudo-labels of GO prediction probability from individual domain terms. Then, we derived the dense representation of domains consistent with functional information to characterize protein sequences and used the representation to predict protein functions. The embeddings learned both at the domain and protein level have turned out to be functionally meaningful as the embedding distance showed substantial negative correlations with functional similarity29 of GO terms that are present in the domains and protein sequences. Moreover, a systematic comparison with large-scale Protein Language Model (PLM) representations31, which use variants of Transformers32 and BERT33 architectures, and have demonstrated success in function prediction35, revealed that our embeddings are more applicable for function prediction, despite being a fraction of the aforementioned PLM complexity. This improvement is further vividly observed in challenging cases of predicting rare and more specific functions. In addition, using a straightforward K-Nearest Neighbors (KNN) model with the learned embeddings along with sequence similarity and interaction information, Domain-PFP remarkably outperforms more complex state-of-the-art methods. Most notably, Domain-PFP achieved an increase in the area under precision-recall curve (AUPR) by 2.43%, 14.58%, and 9.57% over the state-of-the-art method for molecular function (MF), biological process (BP), and cellular components (CC), respectively. Domain-PFP has also demonstrated competitive performance when compared with top-scoring methods in the CAFA3 evaluation36.Here, we introduce Domain-PFP, a protein function prediction method that uses functional representation of proteins through domain-GO association learned by a self-supervised method from protein databases. Self-supervised learning is based on the idea of leveraging the inherent co-occurrence relationship of complementary information in the data to learn new labels in a semi-automatic process37 and assigned InterPro domains using InterProScan 5 REST API38. Despite InterPro maximizing domain coverage by combining entries from 13 databases, 36,403 proteins had no InterPro annotations, so we discarded them. Concurrently, we collected GO terms for protein sequences from UniProt. We considered both experimentally and computationally assigned functions since IEA (Inferred from Electronic Annotation) terms demonstrated increased accuracy in our previous works6. We also propagated the parent GO terms using the core ontology release 2021-01-01. In summary, our dataset contained 531,599 proteins with 32,471 unique domains and 33,199 unique GO terms .We collected 568,002 protein sequences from Swiss-Prot (release 2022_3)domaini having the GOj function:Using the domain and GO term assignments to protein sequences, we computed the conditional probability of a protein that contains Here, Our ultimate goal is to predict protein functions. To achieve this, we aim to develop a representation of domains that, in conjunction with a learned representation of GO terms, is consistent with the domain-GO co-occurrence conditional probability. In other words, we seek to design two representations or embeddings, W1, b1) and  are weights and biases from the first and the second layer of the network, respectively. The Hadamard product of the two embeddings is represented by the symbol 39. We intended to keep the function 40. The function In our case, we utilized two 256-dimensional embedding matrices mentclass2pt{minimThe overall pipeline for learning the domain embeddings is summarized in Fig. 31. For a protein Using the computed domain embeddings, we represented a protein, which may be composed of several domains, as the average of the embeddings of all the domains in it. This is similar to how PLM encodes proteins by averaging the individual residue level representations21. KNN models using protein language models have also been shown to be on par with top methods of Critical Assessment of Functional Annotation 3 (CAFA3)34. The confidence score of annotating a protein With the protein embedding, we can use supervised classifiers to infer protein functions. Here, we used a KNN classifier, following the convention of BLAST or PPI network scoring38, and their individual domain embeddings are obtained. The embedding of the query protein is then computed by taking the average of the assigned domain embeddings  and GO:0004866 (endopeptidase inhibitor activity) both with a high probability of 0.9 by DomainGO-prob. The GO term GO:0004869 in the MF category represents binding to and preventing the activity of cysteine-type endopeptidase. Looking at the domain structure, IPR000010 has three subdomains, among which only one subdomain, IPR025764, a Fetuin-B-type cystatin domain, has an annotated GO term with experimental evidence, GO:0004866 (endopeptidase inhibitor activity)46. From this domain hierarchy, in addition to GO:0004866, a child term, GO:0004869 with an ‘is a’ relationship with GO: 0004866, was correctly transferred to IPR000010 by DomainGO-prob.The first example Fig.  is IPR00The second example is a recovered annotation of a CC term, GO:0005634, which represents nuclear localization, with a probability of 0.99 assigned to IPR000690. In InterPro2GO, GO:0005634 is the only CC term associated with this domain. IPR000690 is Matrin/U1-C, C2H2-type zinc finger, which co-occurs with the homologous superfamily IPR036236 in 86.6% of protein sequences Fig. . IPR0362The next example in Fig. 47 and thus has the GO:0006508 function, which was derived to IPR000081. It should be noted that despite IPR009003 completely overlapping with IPR000081, DomainGO-prob did not associate IPR009003 with viral activity (GO: 0016032). For the domain IPR009003 DomainGO-prob predicted a small probability of 0.33 for GO:0016032 , which was likely induced from the several co-occurring domains involved in viral activities, for example, IPR007094, IPR002527, IPR014838. On the contrary, the actual function for IPR000081, i.e., GO:0006508 was predicted with a probability of 1.0. Therefore, for this example DomainGO-prob was capable of contrasting between complementary information.Some domains are responsible for multiple different functions. For example, the domain IPR000081, which has just been analyzed for viral activity in the previous example, was also correctly assigned with proteolysis (GO:0006508) by DomainGO-prob with a predicted probability of 1.0 Fig. . However48. Therefore, proteins from this family are annotated with the function GO:0016494 (CXC chemokine receptor activity). Since Chemokine receptors are part of the G protein-coupled receptor (GPCR) family, proteins from the IPR000174 family  are also members of IPR000276  and have the IPR017452  domain. Although this context provides information about the GPCR family, it is difficult to narrow it down to the CXC family, without individual precise information. This precise information is absent in our adversarial mode of training. As a result, DomainGO-prob predicted a low score of 0.34 for GO:0016494 but managed to assign GO:0004930 (G protein-coupled receptor activity) to IPR000174 with 0.95 probability from the co-occurrence of IPR017452.There are cases where DomainGO-prob failed to associate GO terms to domains. For instance, in Fig. 49. The 12 PLMs we compare against are ProtT5-XL30, ProtALBERT30, SeqVec50, ProtBERT-BFD30, ESM-1b31, ProtXLNet30, TAPE-BERT-PFAM51, CPCPProt52, MSA-Transformer53, UniRep54, Learned-Vec55, and ProtVec56. These PLMs were trained on unsupervised tasks such as predicting a segment of masked residues given the rest of the protein30 or predicting the next residue from all the residues before it50, on a large protein sequence dataset, e.g. the entire UniProt. Supplementary Table We evaluated the performance of DomainGO-prob embedding in comparison with 12 large Protein Language Models (PLMs) following the benchmark study performed by Unsal et al.rd, 2/3rd and bottom rest, respectively). Therefore, based on frequency and specificity, 3 × 3 = 9 groups of GO terms can be constructed for the three GO categories, i.e. 3 × 9 = 27 groups. Among them, as there were no GO terms that fall under the high-specific group, the benchmark ended up with 25 groups. For each group, at most 5 GO terms were selected based on dissimilarity according to the Lin’s similarity measure42, which resulted in a total of 117 GO terms to predict. The PROBE dataset contains 19,995 human proteins clustered at a 50% identity cutoff and only experimental GO annotation. The human proteins falling under these criteria were used for benchmarking GO function prediction by undergoing a 5-fold cross-validation test. Unsal et al. provided a convenient CodeOcean distribution , where given the embeddings of the test proteins, GO predictions are made, and the performance is evaluated on the PROBE dataset. We used it to test our DomainGO-pair-based protein embedding  and specificity  networks employing a graph convolutional neural network. NetGO2.016 is an all-encompassing ensemble method that incorporates BLAST, domain, PPI, GO term frequency, PubMed publications, and sequence information both in form of k-mers and embedding. Among the existing methods, NetGO2.0 has shown the highest evaluation values for MF and the best Smin value in BP36 .DeepGOPlusj for protein i from BLAST and PPI information are defined asIn the latter half of Table 58, and edge weight from STRING PPI network (ver. 11.0)59, respectively. We used the same STRING version as DeepGraphGO21.Here, The final score is a simple average of the terms from the three sources:max, AUPR, and Smin36 (see Methods). Fmax computes the maximum possible protein-centric F1 score, overall prediction thresholds. AUPR, the area under PR curve, on the other hand, is a suitable metric for imbalanced data and penalizes the false positive predictions, which is highly applicable to function prediction16. Finally, Smin is a measure of semantic distance between predicted and actual annotation, based on the information content of the individual GO terms18, i.e., this metric indicates the capability of predicting rare GO terms.We compared the performance of the methods using the three CAFA evaluation metrics, namely Fmax, AUPR, and Smin in all the three sub-ontologies. Notably, Domain-PFP achieved an AUPR of 0.697 for CC, whereas DeepGOZero, a recent method based on domain information scored 0.645, i.e., a large improvement of 0.052. In terms of Fmax, Domain-PFP outperformed DeepGOZero and DeepGOCNN by achieving 0.013–0.014 and 0.051–0.086 higher scores, respectively.Firstly, we compared Domain-PFP with sequence-only or domain-based methods, e.g., DeepGOCNN and DeepGOZero. This is a fair comparison as the base Domain-PFP uses only domain information which is inferred from sequence information. It can be observed from the table that Domain-PFP outperforms these methods in terms of Fmax for MF. Fmax for BP increased from 0.41 to 0.434, and AUPR for CC increased from 0.697 to 0.717. Furthermore, Domain-PFP with BLAST consistently outperformed DeepGOZero+BLAST, which also uses the same information, in all 9 metrics. For example, DeepGOZero+BLAST achieved AUPR scores of 0.665, 0.356, and 0.654 for MF, BP, and CC, respectively, whereas Domain-PFP + BLAST achieved 0.693, 0.367, and 0.717, representing improvements of 0.028, 0.011, and 0.063, respectively. When compared with DeepGOPlus or TALE + , both of which use BLAST, the improvements made by Domain-PFP + BLAST appeared consistent as well.Adding different features generally improves the performance of function prediction. When BLAST information was combined, Domain-PFP improved the overall performance, except for a slight drop of 0.001 in F16, where the authors reported that PPI information performed better than domain information for predicting BP terms but not for MF and CC terms. For example, the Fmax of MF and CC dropped by 0.009 and 0.002, respectively. Despite this, Domain-PFP + PPI still outperformed DeepGraphGO, a method using domain and PPI information in a much more sophisticated graph neural network, in 5 out of 9 metrics.Next, we experimented with including PPI information with Domain-PFP. However, this only improved the performance in BP, as expected, since BP involves multiple related and interacting functions that can be captured by PPIs. On the other hand, the performance of MF and CC was negatively affected. This situation is similar to the findings of NetGO2.0max and AUPR of BP improved by 0.042 and 0.049, respectively. This integration of BLAST and PPI features enabled Domain-PFP to consistently perform superior to all the existing methods. For example, the current state-of-the-art method NetGO2.0 was surpassed by Domain-PFP in 8 out of 9 metrics (except for Fmax for MF). In terms of Fmax for BP and CC, Domain-PFP achieved 0.021 and 0.024 higher scores, respectively. For AUPR, the improvements were 0.017, 0.050, and 0.060 for MF, BP, and CC, respectively. Similarly, in terms of Smin, Domain-PFP + BLAST + PPI achieved 0.041, 0.784, and 0.389 smaller scores for MF, BP, and CC, respectively, implying that non-trivial GO terms were captured better.Finally, we experimented with integrating both BLAST and PPI simultaneously. This brought improvements in all the metrics except for AUPR of CC. Notably, Fmax for MF. which we hypothesize is due to the inclusion of Pubmed publication information that is likely to contain precise information vital for MF prediction.This comparative evaluation with state-of-the-art function prediction methods further supports our self-supervised approach of learning functionally informed representations for protein domains. We observed that a simple KNN model with DomainGO-prob embedding not only outperformed more sophisticated deep learning models  but also methods with access to more information sources . The only case where we fell behind the previous state-of-the-art, NetGO2.0, is in Fmax of MF, where NetGO had the highest score. Compared to Fmax, the improvement in AUPR is more prominent, which can also be observed in the results presented in Table In our evaluation, we have utilized the benchmark compiled by the authors of DeepGOZero, which was derived from the NetGO benchmark dataset, following protocols similar to CAFA. Using this benchmark allowed us to compare our performance against the other recent methods, that were evaluated on this benchmark by the authors of DeepGOZero. We also evaluated Domain-PFP on the original NetGO benchmark. The results of those experiments are presented in Supplementary Table 8 and GAT-GO60. These methods use 3D protein structure information in a graph neural network and protein sequence information with a language model. Both methods were evaluated on a common benchmark dataset, composed of 29,902, 3,323, and 3,416 proteins for training, validation, and testing, respectively. The train and test proteins possess a total of 2,752 GO terms and they are clustered with 40% sequence identity.To assess the performance of Domain-PFP against structure-based protein function predictors we considered two recent methods DeepFRImax in CC and AUPR in MF. The performance of Domain-PFP was further improved by including BLAST predictions, which results in the best score for all the metrics.We retrained Domain-PFP on this dataset and observed the performance across the three sub-ontologies. The results are presented in Supplementary Table 36. We trained the network model of Domain-PFP using the CAFA3 training dataset and evaluated the results using the official evaluation code. The training dataset comprised 66,841 protein sequences annotated before September 2016, with 677, 3992, and 551 MF, BP, and CC GO terms, respectively . For MF, our Fmax score, 0.59, was second to Zhu Lab (Fmax: 0.62), with a substantial margin to the next method, orengo-funfams (Fmax: 0.54). The top method by Zhu Lab combined more diverse information using an ensemble approach, including sequence, domain, homology, biophysical information, which likely gave that a competitive edge, similar to NetoGO2.0. We also mention that both DomainPFP and DomainPFP+BLAST showed higher Fmax scores than DeepGOPlus, which reported Fmax scores of 0.557, 0.390, and 0.614 for MF, BP, and CC, respectively, in their paper18.The results of Domain-PFP on the CAFA3 benchmark are presented in Fig. 61. Our approach is consistent with this definition as we first use the domain-go association probabilities as pseudo labels, which initializes our domain embedding parameters; then, we use this embedding later in a supervised learning protocol and we predict the functions of the proteins. This strategy also holds in the benchmarks on the NetGO and CAFA3 dataset we performed. To the best of our knowledge, this work is the first to apply self-supervised learning in the domain of protein function prediction. Based on co-occurrence contextual information between domain and GO terms, we devise embeddings for domains so that functionally related domains have similar embeddings. Since co-occurrences were learned from entire protein sequences, the domain embedding, DomainGO-prob, encodes GO associations that are not explicitly described in the domain database. Remarkably, our rather simple model, Domain-PFP, along with BLAST and PPI information, demonstrated superior performance over all state-of-the-art function predictors.Despite protein domains carrying the functional signatures of proteins, they have not been used to their full potential to date. Look-up-table-based domain to GO assignments tend to lack coverage. On the other hand, deep learning-based approaches using domains as high-dimensional input suffer from limitations in training data and information loss in network bottlenecks. Therefore, our motivation has been twofold: improving coverage and reducing information loss. Based on recent advancements in self-supervised learning, it has become motivating to apply such concepts in protein domain learning to alleviate these issues. Our method follows one of the core concepts of self-supervised learning where pseudo-labels are first learned to initialize model parameters, which are then used to perform the actual task using a supervised or unsupervised method13. To address these, attention mechanism maybe applicable. These are improvements we wish to explore in our subsequent works. In the current work, we practically alleviated these issues by augmenting with BLAST and PPI information-based predictions.One likely limitation of this work could be the case of unknown domains. All existing methods based on protein domains fail to predict anything if the domain seen during inference was absent in the training data, in which case they predict a default value. This limitation can possibly be resolved by generating the functionally aware domain representation and localization end-to-end from the protein sequence directly using a larger deep learning model. Another limitation is that the current protein embedding considers domains in a protein equally Eq. , althoug31, which were shown to perform well in protein tertiary structure prediction and other tasks. Additionally, we wish to analyze the suitability of our model in a zero-shot learning scenario. Specifically, our goal is to train DomainGO-prob on pretrained GO embeddings based on GO tree hierarchy and observe if GO terms absent in the training data can be retrieved this way.Another possible future direction could be to combine with general protein language modelsp = 0.05) and activated by RELU. Finally, we use a linear layer to predict the We have designed a neural network to learn the domain-GO co-occurrence conditional probability distribution Fig. . The dom62, we have a comparatively much larger number of domain-GO terms out of context, i.e., 39 with a learning rate of 0.001 (the other parameters were kept as default) and a batch size of 163,840 for 200 epochs. 20% of domain-GO pairs, which were randomly selected, were used as the validation set. The experiments were performed 10 times and the best model based on validation performance was selected.Similar to word2vec embedding training63. 42:1 and GO2 are explored to maximize the score and p(GO) is the probability of GO term in the entire Swiss-Prot database. Then, a set of GO annotations in a GO category for two proteins, a and b, are defined asGOscore from the three GO categories.Finally, 49, we used Weighted F1 Score as the evaluation metric. The values were computed using their official CodeOcean distribution.For the PROBE benchmark, similar to the original benchmark by Unsal et al.max, Smin, and AUPR2. We used the same evaluation codes as used by22 to ensure consistency.To compare with state-of-the-art methods, we used the CAFA protein-centric evaluation metrics Fmax is the maximum possible protein-centric F1 score, computed over all prediction thresholds.FHere, The area under precision-recall curve, i.e., AUPR score is computed from the computed precision and recall scores using the trapezoidal rule.Smin is a measure of semantic distance between the ground truth and prediction annotations based on information content of the GO classes. The information content The two terms remaining uncertainty Smin is computed asThe value of Peer review fileSupplementary InformationReporting-Summary


The chemical composition, antioxidant properties, and sensory aspects of sponge cakes with the addition of flours from edible insects  were evaluated. The addition of edible-insect flours increased the protein, fat, and dietary fiber content in all cases. The utilization of edible insects demonstrated a notable augmentation in the phenolic compounds . This resulted in an increase in the antioxidant activity measured against the ABTS radical cation, the DPPH radical, and ferric ions. The antioxidant potential, assessed by four different methods, unequivocally confirmed that the aforementioned polyphenolic compounds found in edible insects provide significant radical-scavenging and antioxidant activity in sponge cakes containing them. The polyunsaturated fatty acid contents were significantly lower in cakes with insect flour compared to the standard wheat cakes. Products and raw materials exhibited high values of the n − 6/n − 3 ratio, which may be associated with negative health effects, with a high oleic acid content. The amino acid score (AAS) for the essential amino acids exceeded 100% for all obtained products. The sponge cakes were accepted by consumers and the taste was the most important predictor for overall acceptability, whereas the structure and appearance had less impact. An increasing number of institutions are emphasizing the importance of a sustainable food economy. The rising population is exerting greater pressure on ecosystems as a result of heightened demand for food, a fundamental human requirement ,2. One oTenebrio molitor L.), house crickets (Acheta domestica L.), migratory locust (Locusta migratoria), and, commencing from 5 March 2023, the larvae of the buffalo worms (Alphitobius diaperinus P). The Commission Implementing Regulation (EU) 2017/2470 was released on 30th December 2017. This regulation establishes a European Union list of novel foods in accordance with Regulation (EU) 2015/2283 of the European Parliament and Council on novel foods . In addition, the European Commission’s Catalogue of Novel Foods provides information on individual component statuses. This catalog contains the names of food ingredients and the information available at the time regarding their status; it is not a definitive guide [Approximately 2300 insect species are edible. However, currently, the European Union (EU) permits only four insect species that comply with the Novell Food Regulations (Reg. 2015/2283) for human consumption. Among them are the larvae of mealworms (ve guide .Acheta domestica L.) is an insect whose adult form (imago) is used for feed or food. Similar to the previously mentioned insects, it can be widely used for the supplementation of pastry products [In the case of insects such as mealworms or buffalo worms, their larval form is used for food purposes. The dried and ground larvae of these insects contain about 45–49% protein and 14–28% fat , proteinproducts  and the products .Edible insects are a good source of protein and fatty acids , and alsTenebrio molitor L., Acheta domestica L., and Alphitobius diaperinus P.) on the physicochemical, functional properties, and consumer acceptance of sponge cakes supplemented with the addition of them. The research hypothesis assumes that the addition of the abovementioned edible-insect meals will increase the nutritional value of the obtained products, while maintaining consumer acceptance at an appropriate level.The aim of this study was to determine the effect of the powders of three species of edible insects (Tenebrio molitor (TF) ; buffalo worm, Alphitobius diaperinus (BF) ; cricket, Acheta domesticus (CF) . Sponge cakes were obtained under laboratory conditions.Sponge cakes (S) and sponge cakes in which part of the pure refined wheat flour  was replaced with an appropriate insect flour at a ratio of 15% and 30% of the original weight of the wheat flour were used. The following insect flours were used—mealworm, The sponge cakes were made using the cold method with an eggs:sugar:flour ratio of 2:1:1 (2 kg:1 kg:1 kg). The dough was prepared using an Aristan 7 mixer , as follows: in the mixing bowl, the egg whites were whipped for 5 min (speed level 10), powdered sugar was added and whipped for 3 min (speed level 8), and the egg yolks were then added and mixed for 1 min (speed level 3). Sieved flour was then added and mixed for 1 min (speed level 2). The dough was formed using a confectionery sleeve into silicone-cake-tin (30 mm diameter) cakes. The cakes were baked in a Miwe roll-in oven (Germany) at 180 °C for 15 min. Cakes were cooled down for half an hour at room temperature and used for further analyses.The wheat and edible-insect flour were assessed for the following parameters: ash content (AOAC 923.03) and protein content (AOAC 950.36), with the protein content calculated using an appropriate conversion. In the case of the standard sponge cakes, a conversion factor of 6.25 was used, while in the case of products containing insect flour, conversion factors of 6.25 and 4.76 were used in accordance with the proportions of the individual ingredients in the recipe . The cruAmino acid analysis was performed according to the method of Moore and Stein 1951) , Davidso51 , DaviThe protein nutritional value was assessed by calculating the amino acid score (AAS) in accordance with FAO/WHO guidelines, based on the quantity and composition of the amino acids  (Equatio the FAO  (2013).3 methanol solution) of the fat sample were performed. The methyl esters were then transferred to the organic phase (hexane). This process was supported by the addition of a saturated NaCl solution. The fat phase was collected into vials and analyzed using a Shimadzu GC2010Plus chromatograph  with a flame ionization detector (FID). The operating parameters were as follows: FID detector temp. 240 °C; temperature dispenser 240 °C; oven temp. 195 °C to 240 °C (5 °C/min) . An SH-FAME column (30 m–0.32 mm–0.25 μm) was used, and the carrier gas helium was 1.6 mL/min. The split ratio was 100. Individual fatty acid methyl esters were identified by comparison to the standard mixture of the Supelco 37 component FAME Mix and of CLA isomers . The analyses were performed in four repetitions.The fat fraction was obtained according to the AOAC method 935.38, while the determination of the total fatty acid profile was performed according to the AOAC-approved method 991.39  . To obtaL = brightness difference;Δa = redness difference;Δb = yellowness difference.ΔThe color of the bread crust and crumb was assessed employing the CIELab  system using the Konica Minolta CM-5 spectrophotometer . A measurement angle of 10° and an illuminant of D65 with an 8 mm shutter were used. Ten different locations on the crust and crumb surface were measured to ensure accuracy. The test temperature was maintained at 21 °C throughout. The average color parameters obtained from the measurements were utilized to compute the overall color variation of wheat bread as determined by the formula  (Equatiog) . The supernatant was decanted and stored at −20 °C for further analyses.The extraction procedure: approximately 0.6 g of the sample was shaken in 30 mL of 80 g/100 g ethanol for 120 min . The obtained extracts were centrifuged  and stored for 30 min in the dark. The absorbance was measured at 760 nm using a Helios Gamma 100–240 spectrophotometer . The results were reported in mg catechin/100 g of dry matter of the sample.The Folin–Ciocalteu reagent method, as described by Singleton et al. , was useThe flavonoid content was determined using the spectrophotometric method described by El Hariri et al. , using tThe free-radical-scavenging activity of the samples was measured using the 2,2-diphenyl-1-picrylhydrazyl (DPPH) according to the method of Sánchéz-Moreno et al. . The ext+• stock solution was diluted with PBS buffer to obtain an Abs of 0.700 ± 0.05. Volumes of 2.00 mL of the ABTS+• were added to the diluted sample extracts. The ABTS+• bleaching was monitored at 30 °C and the discoloration after 6 min was used as the measure of antiradical activity. The bleaching rate of the ABTS+• in the presence of the sample was monitored at 734 nm using a Helios Gamma 100–240 spectrophotometer . The results were expressed in mg/g Trolox equivalents Antiradical activity, using the synthetic radical cation ABTS, was determined according to Re et al. . The radThe Oyaizu method  was used2. The solution was mixed for 30 s, and then 100 µL 5 mM ferrozine was added. The reaction mixture was mixed and left to stand at 23 °C for 15 min. The absorbance of the solution was estimated by the spectrophotometric method at 562 nm with a Helios Gamma 100–240 spectrophotometer . A calibration curve was constructed using disodium ethylenediaminetetraacetate dihydrate (EDTA). The results were expressed as mg EDTA/g.The chelation of Fe(II) ions by the ethanol extracts was determined as described by Gu et al. . An amouThe analysis of volatile flavor compounds using an electronic nose (e-nose) was conducted following the method described by Kowalski et al. .Instrumental taste analysis of the tested samples was carried out using the Alpha MOS ASTREE II electronic tongue (e-tongue) from Alpha MOS, Toulouse, France, according to the method described by Kowalski et al. . The e-t−1 and then cooled to 15 °C. The analysis was performed in triplicate. The onset (To), peak (Tp), and conclusion (Tc) temperatures, depolymerization temperature range of the RS starch ΔT = (Tc − To), and enthalpy change (ΔH), expressed in J g−1 sample, were calculated from thermograms.The thermal properties of the sponge cakes were determined by differential scanning calorimetry (DSC) . For thiThe sponge cakes were offered to participants right after they were baked. The study comprised 64 volunteers aged between 19 and 23 years, chosen from the Medical University of Gdańsk’s database of willing participants. Only those without food neophobia were included in the study. Each sponge cake variety, including the control sample, was tested for acceptability on alternate days. The study was conducted as a double-blind study. Each probant received one biscuit with an assessment card, which was appropriately coded. Each participant received a unique code to facilitate the compilation of data from all days. The subjects knew that they were sponge cakes with the addition of insect flour, while the amount of the additive and the type of edible insect were not known to the probants or the staff who conducted the study. The respondents were healthy, did not take any medications or supplements, did not follow any special diets, and did not smoke cigarettes. All participants provided informed consent to take part in the study, which was approved by the Independent Institutional Research Ethics Committee at the Medical University of Gdańsk (NKBBN/346/2021). Prior to the study, an assessment of food neophobia was conducted on all subjects using the Food Neophobia Scale (FNS) . Appearap ≤ 0.05. In cases where the Levene test indicated significant differences, a post hoc least-significant-difference (LSD) Fisher’s test was conducted. The mean ± standard deviation was used to present the results. During the planning phase of the experiment (on the acceptability of the sponge cakes made with insects), an investigation was conducted into the sample size selection at a level that could produce a statistical conclusion with adequate accuracy and confidence. The probability of detecting the effects of a specific size through test power analysis and interval estimation was also explored. The parameters of multiple regression were estimated using the REGLINP command in an Excel 2010 PL spreadsheet considering the concept of shared variability.Statistica 13.0, developed by Tibco Software in Palo Alto, was utilized to conduct the statistical analysis. Sponge cake features were tested through a two-way ANOVA on the flour type, percentage of substitution, and their interaction, with a significance level of The chemical composition of food determines its nutritional value, which affects its usefulness in human nutrition. Both the raw materials and individual sponge cakes differed in the content of specific nutrients . Insect Insect flours were characterized by a significantly higher content of all essential amino acids compared to the wheat flour . Sponge In the fatty acid profile, both insect flours and sponge cakes with their inclusion were characterized by the dominance of monounsaturated fatty acids (MUFAs), ranging from 38.78 in CF30 to 47.97 g/100 g in TF15, and saturated fatty acids (SFAs), ranging from 34.38 for BF30 to 38.27 g/100 g for CF30. The addition of insect flour as an animal-derived ingredient contributed to a reduction in the nutritional value of the final product. Except for the BF15, TF15, and TF30 sponge cakes, the MUFA content in the sponge cakes was significantly lower compared to the standard. Furthermore, the PUFA content and the ratio of total PUFAs to total SFAs were significantly lower in the sponge cakes with the insect flour compared to the standard, except for the BF30 sponge cakes. The use of insect flours also led to a significant increase in the n6/n3 ratio . The recHowever, evaluating the nutritional value of insect lipids based solely on fat indexes and the ratio of individual fractions is challenging, as certain fatty acids, like oleic acid, found in higher amounts in sponge cakes with edible-insect flour, have been shown to have beneficial effects on insulin sensitivity . Oleic aColor is one of the attributes of bakery products, such as cakes, that can influence consumer acceptance. The addition of insect flour has contributed to significant changes in the CIELab parameters and total color change compared to the standard sponge cakes . Insect The characteristics of the raw materials used (insect flours) were presented in a previous publication by Gumul et al. . The utip-coumaric acid (hydroxycinnamic acids), and protocatechuic aldehyde (hydroxybenzoic acids), were detected , TPC, and DPPH (R2 = 0.939), as well as between TPC and FRAP (R2 = 0.925), and TPC and iron reduction (R2 = −0.859). Furthermore, it can be suggested that, in addition to polyphenols, newly formed compounds during the baking process, such as Maillard-reaction products, may also contribute partially to the high radical-scavenging and antioxidant activity observed [A strong positive correlation was observed between the total polyphenol content (TPC) in the analyzed sponge cakes and ABTS  were grouped into the third cluster due to their noticeable deviation in relation to the other examined samples, particularly with regard to their umami and bitter taste. The correlation between the increase in umami, bitterness, sourness, saltiness, and sweetness, and the substitution of wheat flour with insect flour, may be associated with the relatively higher protein, mineral, and organic acid content in the insect flours as compared to the wheat flour. Consequently, the findings of this study suggest that the composition and quantity of ingredients used in the production of sponge cakes could influence their sensory properties.Based on the obtained results of thermal analysis of the tested products, it was noted that a single peak was visible in the obtained endotherms in the temperature range from approximately 45 °C to 160 °C, indicating the presence of resistant starch (RS) in those products .Depending on the type of flour used, and its proportion in the recipe, it was found that the amount of RS formed  in the sponge cakes ranged from an average of 18% to 53%  higher compared to its content in the control sample without insect flour. A significant impact of the type of insect flour used on the amount of RS formed was demonstrated. The highest amount of RS was present in sponge cakes with the mealworm flour, followed by the buffalo worm and cricket flours, regardless of the concentration of these flours. The obtained ∆T values indicate that the RS in the sponge cakes produced with insect flours has a less-crystalline structure compared to the ∆T value obtained for the control sample, suggesting a different influence of the present components in the insect flour, such as proteins and fats, on the retrogradation process of starch. It is known that the interaction between starch and certain nonstarch components, including proteins and lipids, may affect the formation of RS, which exhibits health-promoting properties. It has been observed that protein, as the main food component, plays a significant role in reducing starch digestibility, similar to other components of the food matrix, such as hydrocolloids and phenolic compounds, partly by forming complex compounds with starch .The ANOVA results indicate that the quantity of the additive had a significant impact on several sensory assessment factors, whereas the type of additive did not. Only the structure of the sponge cake was affected by the type and quantity of the additive. It is worth noting that the assessed attributes were mainly influenced by the quantity of the additive and not by the type used. Sponge cakes without the addition of insect flour received the highest score from respondents (6.19), while the acceptance for sponge cakes with the insect flour substitution was lower, ranging from 4.63 to 5.56. Increasing the content of the added meal resulted in lower ratings for all parameters assessed by the evaluation team. Equations were formulated using the component factors that influenced the acceptability for every variant analyzed in the data study to establish which of the examined sensory parameters had the most significant effect on overall acceptability. 2 measured for all tested samples was high at 0.99, thereby highlighting the model’s ability to explain almost 99% of the dependent variable’s variability. The remaining 10% of the variability was attributed to unanalyzed parameters. The regression analysis identified taste as the critical factor in determining the overall acceptability. It was observed that the greater the inclusion of insect meal, the lower the taste rating. The high x1 coefficient, exceeding 0.5 each time (0.73 for T. molitor), made the taste the most important element in determining acceptability and the final rating set by the testers.Preliminary regression analysis indicated that the results of the sensory characteristics can be generalized by omitting the amount of added insect flour. Multiple regression analysis showed that, for sponge cakes with the addition of insect meal, the smell turned out to be insignificant and had no effect on the overall acceptability of the tested sponge cakes, or had only a slight effect. The results obtained demonstrate that the acceptability level was determined by the predictors incorporated in the regression equation, with taste being the most significant factor for overall acceptability, followed by structure and appearance, to a lesser extent. The correlation coefficient RT. molitor flour. However, they did not find any significant impact on overall product acceptability when varying the additive level (5% and 10%). In the authors’ previous study [The current results find partial confirmation in the literature. However, sensory evaluation depends on the type of product and the amount of additive used. Roncolini et al.  observedus study , a decreus study  observedThe addition of insect flours had a significant impact on the nutritional properties and consumer acceptance of the obtained sponge cakes. Both the raw materials and sponge cakes exhibited high values of the n-6/n-3 ratio, indicating an imbalance in the lipid fractions; however, with a relatively high oleic acid content. For all the analyzed sponge cakes’ essential amino acids, the AAS exceeded 100%. The range was from 100.15% (lysine in CF30) to 216.43% (for AAA in the TF15 sample). The introduction of edible insects to the biscuit recipe also increased their antioxidant potential, although one should be aware that this type of addition will not be crucial in increasing the antioxidant value of the product as much as plant additives. Sponge cakes supplemented with flour from edible insects are also characterized by an increase in the content of dietary fiber. This increase is not only due to the fiber content of the flours themselves, but also due to the interaction with starch and the formation of resistant starch. Products with the addition of edible insects are generally well-accepted by consumers, and the most important quality factor affecting acceptance is taste. The conducted research indicates that the use of edible insects in the form of flours added to confectionary products may both gain consumer acceptance and contribute to the improvement of the prohealth properties of these products.


Hand, foot and mouth disease (HFMD) caused by a variety of enteroviruses remains a major public health problem in China. Previous studies have found that social factors may contribute to the inconsistency of the relationship patterns between meteorological factors and HFMD, but the conclusions are inconsistent. The influence of social factors on the association between meteorology and HFMD is still less well understood. We aimed to analyze whether social factors affected the effect of meteorological factors on HFMD in Sichuan Province.We collected daily data on HFMD, meteorological factors and social factors in Sichuan Province from 2011 to 2017. First, we used a Bayesian spatiotemporal model combined with a distributed lag nonlinear model to evaluate the exposure-lag-response association between meteorological factors and HFMD. Second, by constructing the interaction of meteorological factors and social factors in the above model, the changes in the relative risk (RR) under different levels of social factors were evaluated.The cumulative exposure curves for average temperature, relative humidity, and HFMD were shaped like an inverted “V” and a “U” shape. As the average temperature increased, the RR increased and peaked at 19 °C . The urbanization rate, per capita gross domestic product (GDP), population density, birth rate, number of beds in health care centers and number of kindergartens interacted with relative humidity. With the increase in social factors, the correlation curve between relative humidity and HFMD changed from an “S” shape to a “U” shape.Relative humidity and average temperature increased the risk of HFMD within a certain range, and social factors enhanced the impact of high relative humidity. These results could provide insights into the combined role of environmental factors in HFMD and useful information for regional interventions.The online version contains supplementary material available at 10.1186/s12889-023-15699-4. Hand, foot, and mouth disease (HFMD) is a common infectious disease caused worldwide by a variety of enteroviruses . People Previous studies have found that HFMD is characterized by seasonal variation, spatial aggregation and spatial heterogeneity -13, whicIn addition, the above studies mainly used a two-stage distributed lag nonlinear model (DLNM) to analyze the explanatory ability of city-specific indicators on the heterogeneity of the association between meteorological factors and HFMD. Due to the features of DLNMs, the above studies could not consider the spatial autocorrelation of HFMD found in other studies . At presSichuan Province is one of the provinces with a serious HFMD problem in China. Since 2008, the reported incidence of HFMD has increased and reached 71.59/100,000 in 2017. Moreover, the annual average reported case fatality rate from 2008 to 2017 reached 42.9/100,000, which ranked second in China . In addiLocated between latitudes 26°03’-34°19’ north and longitudes 92°21’-108°12’ east, Sichuan covers an area of 486,000 square kilometers in southwestern China. It comprises 21 prefecture-level cities, mainly concentrated in the eastern region, and the scale of each city is considerably different  represented different levels of social factors. The flow chart was shown in Fig. Distributed lag nonlinear models based on the cross-basis function were used to explore the nonlinear and delayed associations between HFMD and meteorological factors. According to previous studies and the incubation period of HFMD, we assessed the delayed effects of meteorological factors on HFMD to be 14 days  and consA Bayesian spatiotemporal model was constructed with the daily reported counts of HFMD for all 21 prefecture-level cities in Sichuan from January 2011 to December 2017 as the dependent variable. HFMD counts were assumed to have a negative binomial distribution to account for overdispersion. The spatiotemporal random effect was an independent variable that included the city-level daily autocorrelated random effect and year-specific city-level spatial random effect, accounting for seasonality, unobserved and unmeasured sources of variation and spatial dependency structure, respectively. We added the cross-basis function of meteorological factors and their linear interaction term with social factors to the Bayesian spatiotemporal model to construct the final model , 30. The0.5=0.01 ; \documeWe mainly investigated the influence of relative humidity and average temperature on HFMD. The relative risk and 95% confidence interval (CI) were calculated using the median as a reference value. As the parameter specification and forms of meteorological confounders may influence the effect estimation, we conducted sensitivity analyses , the risk of HFMD was higher in areas with a low population density on lag days 4–10 than in areas with a high population density. When relative humidity was low (≤ 20%), the risk of HFMD was higher in low population density areas on lag days 4–7 but greater in high population density areas after lag day 10. The effect of the number of beds and kindergartens was similar to that of population density, with a higher risk of HFMD in low-level areas during lag days 4–9 when relative humidity was higher. There was no significant difference in the association between average temperature and HFMD under different levels of social factors.We used a Bayesian spatiotemporal model combined with a DLNM to analyze the nonlinear lag associations between average temperature, relative humidity and the risk of HFMD in Sichuan Province and to further investigate the influence of social factors on these associations. Relative humidity and average temperature increased the risk of HFMD within a certain range. The urbanization rate, per capita GDP, population density, birth rate, number of beds in health care centers and number of kindergartens interacted with relative humidity. With the increase in the level of social factors, the correlation curve between relative humidity and HFMD changed from an “S” shape to a “U” shape. Social factors did not have a significant influence on the association of average temperature with HFMD.We analyzed the effect of daily average temperature on HFMD. The cumulative relative risk curve for average temperature approximated an inverted "V" shape, and the highest cumulative RR peaked at 19 °C. This result is consistent with the results of Guilin, Wuhan et al. , 32, 33.We found that the relationship between relative humidity and HFMD varied under different levels of social factors. As the level of social factors increased, the correlation curve between relative humidity and HFMD changed from an "S" to an approximate "U" shape, especially the correlation between high relative humidity and HFMD, which changed significantly. The potential mechanism may be related to relative humidity and social factors affecting the biological basis of HFMD epidemics. The source of infection, route of transmission and susceptible population coexist and interact with each other to form the epidemic process of HFMD. When the number of HFMD immune population decrease and susceptible people increase, the greater the susceptibility of the population, and the more conducive it is to the prevalence of HFMD. In addition, the complex transmission routes of HFMD provide multiple ways for pathogens to change hosts and increase the chance of contact with susceptible populations.The urbanization rate and population density are closely related to the susceptible population and transmission route of HFMD. The results showed that under high relative humidity conditions, the cumulative relative risk of HFMD was higher in areas with high urbanization and high population density, which may be caused by the following two reasons. First, a higher urbanization rate means that more people migrate to cities, including a large number of susceptible people such as children , resulti. suggested that the effect of health resources on the association of relative humidity with HFMD may be related to the increased number of reported cases [Per capita GDP and the number of beds in health care centers reflect the regional economic level and the availability of regional medical and health resources . In geneed cases . Compareed cases . In addiAn increased birth rate implies more newborns in the whole population, increasing the susceptibility in the general population, which in turn strengthens the effect of relative humidity. In regions with a low level of social factors, the cumulative relative risk of HFMD gradually decreased as the relative humidity increased over approximately 82%. The exact mechanism is still unclear. Other unknown or unmeasured factors may be involved, such as dominant HFMD serotypes. Previous studies found that dominant HFMD serotypes vary between prefecture-level cities in Sichuan Province , and theThis is the first study to analyze the influence of social factors on the association between meteorological factors and HFMD based on the combination of a Bayesian spatiotemporal model and DLNM. The influence of meteorological factors on HFMD was stratified according to the gradient of social factors, and the temporal and spatial dependence of HFMD was considered by including spatiotemporal random effects. Our findings provide information for evaluating the risk of HFMD in region-specific social and natural conditions. A limitation of our study is that due to the unavailability of data, the social factors analyzed in our study did not include specific local preventive control measures or policy-related indicators, which are very important for the HFMD epidemic. In follow-up studies, we will consider how to quantitatively evaluate preventive control measures in various places and then estimate their impact on HFMD.In general, we explored the association of meteorological factors with HFMD in Sichuan Province from 2011 to 2017 and the variations in their associations with HFMD under different levels of social factors. We found that social factors  enhanced the influence of high relative humidity on HFMD transmission. The results of our study are helpful for understanding the comprehensive effects of social and meteorological factors on HFMD and provide information for formulating appropriate intervention strategies in regions with different levels of social factors. For example, for areas with a high urbanization rate, such as Chengdu, we should strengthen active surveillance of HFMD during periods of increased relative humidity. At the same time, we can increase HFMD advocacy work for key places such as kindergartens and prepare in advance to prevent a possible new epidemic.Additional file 1: Fig S1. Geographic distribution of weather monitoring stations in Sichuan Province. (The base map is from Resource and Environment Science and Data Center). Fig S2. Effect of degrees of freedom to exposure-response relationship on model (a) average temperature; (b) relative humidity. Fig S3. Cumulative effects of average temperature and relative humidity on HFMD under different degrees of freedom for exposure response relationship. Fig S4. Cumulative effects of average temperature and relative humidity on HFMD under different degrees of freedom for lag response relationship. Fig S5. Scatter plot of meteorological factors and HFMD counts. Fig S6. Sensitivity analysis of the inclusion form of meteorological confounding factors. Fig S7. Temporal changes in the incidence of HFMD and social factors. Fig S8. The correlation between HFMD counts and meteorological and social variables in Sichuan Provence from 2011 to 2017. Fig S9. Cumulative effects of relative humidity on HFMD under different percentiles of social factors. Table S1. Description of daily HFMD counts, meteorological and social variables in 21 prefectures in Sichuan Province.