complex networks  as a unified framework can describe a wide range of systems including the internet and world wide web  , biological systems  and social networks  .dynamical processes taking place on networks , such as information diffusion or epidemic spreading , are strongly influenced by the structure and organization of networks  . for a long time , studies on the interplay between network structure and dynamical processes have been focused on static networks  . recently ,attention has turned to the study of more complicated systems , in which dynamical processes are taking place on temporal networks with time - varying structures  .underlying factors in these systems that drive the evolution of temporal networks can subsequently impact the embedding dynamic phenomenon . identifying these factors andtheir intrinsic association with the process is crucial for unravelling the complexity of these systems , as well as modelling , predicting and controlling the dynamic phenomenon .contact networks are one important instantiation of temporal networks that model either the logical or physical contacts between individuals .examples of the former include long - range communications such as phone calls or email . examples of the latter include colocation - driven short - range communications such as face - to - face human contact  or proximity - based direct wireless transmissions  . unlike logical contact networks , physical ( i.e. colocation ) contact networks are predicated on spatially constrained copresence and depend on mobility for broadscale spreading .the spatiotemporal dynamics of the actors ( nodes ) in such networks are therefore a critical determinant of spreading potential .one of the best available sources of empirical data on colocation contact ( also known as `` encounter '' ) networks comes from electronic mobile wireless device traces  .these traces typically describe either directly recorded encounters between devices  or encounters which are inferred based on mutual presence at a known location  .much work has been devoted to the analysis of these traces , often in terms of their static network - theoretic properties and in some instances also in terms of spreading potential .for example , the authors in  all explicitly analyzed ad hoc  multi - hop message dissemination  facilitated by device mobility and encounters , the latter work being our own performed over the same trace analyzed in this paper .one of the core tools for relating observed spreading behavior of a network quantity ( e.g. virus , information ) to idiosyncratic network features are _ null models _ which separately destroy correlations in a network s contact structure . by simulating spreading on boththe real and null networks one can establish to what extent certain correlations catalyze or impede spreading . prior null models  have focused on _ contact _ shuffling given a set of nodes connected by timestamped links , these models shuffle the links in one of a number of ways to retain certain correlations while destroying others .for example , the authors in  applied null model contact shufflings to a mobile call network ( mcn ) in which nodes were mobile subscribers and links were placed between caller / callee pairs and annotated with one or more call timestamps .a limitation of contact shuffled null models as applied to colocation - based contact networks is that they can not draw any association between spatiotemporal dynamics and spreading .rather , the models consider the contact network independent of the nature of the events which led to the contacts in the first place , such as the movement patterns of individual nodes in colocation contact networks .while many attempts have been made to model such networks , there is yet no structured framework for establishing how nodes spatiotemporal preferences impede or catalyze spreading potential .this paper focuses on exploring the relationship between node spatiotemporal preferences and spreading potential in colocation contact networks . to address this question , we propose an alternative way of generating network null models through a method we refer to as _ inducement _ shuffling shuffle the events on which contacts are themselves predicated and so in the process induce a modified set of contact events .inducement shuffling possesses the attractive property of enabling second - order causal reasoning about spreading behavior . with contact shufflingit is only possible to state how characteristics of the contact network itself influence spreading . with inducement shuffling onecan state how the nature of the events that lead to the contact network in the first place , such as the node movement dynamics , influence spreading .while both shuffling approaches lead to changes in network structure , inducement shuffling explicitly captures the relationships between the node preferences and correlations on one hand , and the spreading potential on the other .we present our inducement - shuffled null models based on the theme of node , location and time which we use to decorrelate spatiotemporal node preferences .we apply the null models to an empirical trace in which ( i ) nodes are mobile wireless electronic devices such as smartphones , tablets and laptop computers ( ii ) locations are access points ( aps ) in a large university campus network and ( iii ) times are the times at which given devices were connected to given aps .contacts in our empirical trace are predicated on device colocation .that is , two devices simultaneously present at a given location are connected by a timestamped link in the inferred contact network . through inducement shufflingwe destroy node s time and location preferences , i.e. we decorrelate the relationships between nodes , times and locations .this in turn leads to a different set of colocation events and thus a modified contact network is induced .for the original and each induced contact network we simulate diffusion of a quantity starting from a randomly infected node under the susceptible - infected ( si ) infection model  . to the best of the authors knowledge ,the present work is the first to take a null models approach to isolating spreading impediments and catalysts in colocation - driven contact networks .more importantly , we believe the inducement - shuffled null models to be the first to enable reasoning about the second - order causal relationship between the events on which the contact network is predicated and subsequent spreading potential . though motivated in the context of a wireless mobile device contact trace , we believe the inducement - shuffled null models presented in this paper may find broader applications in colocation contact networks , some well outside computer networks .our work utilizes a wireless ieee 802.11 ( wi - fi ) network trace collected by the university of queensland ( uq ) australia describing device sessions at individual access points ( aps ) in a large university network over a 14 day period between tue nov 27 17:39:12 aest 2012tue dec 11 17:29:16 aest 2012 .each session record in the uq trace includes ( i ) the unique mac address of the connecting mobile device ( ii ) session start time ( iii ) session end time ( iv ) ap name and ( v ) site .we clean the trace by discarding 1,462 sessions with no end time ( active when trace collection ceased ) and 1 session with zero duration ( start end ) . a further 1,279 sessionsare discarded as specifying no ap . after cleaning ,the uq trace retains 546,260 sessions from 23,895 devices over 3,079 aps at a total of 24 discrete geographic sites . in this paperwe focus only on the largest site in the uq trace the _ st lucia _ campus .the st lucia campus is a large university campus accounting for 445,867 sessions from 20,308 devices over 2,004 aps . after filtering on ( v ) to extract the st lucia trace from the uq trace , we then use ( i)(iv ) to construct the minimum dataset for our analysis which consists of a set of session 4-tuples , each of the form .these 4-tuples fully describe which ( )ode ( mac address ) partakes in a session at what ( )ime ( start and end ) and at what ( )ocation ( ap ) , i.e. they encode the information about the spatiotemporal patterns of nodes .we refer to these 4-tuples simply as the `` session tuples '' from this point onwards .note that nodes and locations just happen to be defined in terms of mac addresses and aps respectively in our analysis .the notion of nodes and locations may be generalized to accommodate equivalent entities specific to the network under consideration .the session tuples extracted from our original dataset and later reconfigured by our inducement shufflings do not explicitly describe contacts between pairs of wireless mobile devices .rather , as is done in  we infer contact from colocation two devices connected to the same ap at the same time are assumed to be in transmission range and so inferred as making `` contact '' .as noted by the authors in  , this inference is an approximation .devices connected to the same ap may not be able to communicate directly , devices connected to different aps may be able to communicate and some contacts take place outside the range of aps .still , it is believed to be a reasonable approximation in the network under consideration .contact inference translates the session tuples into a set of 5-tuples of the form , describing the location and duration of a contact between devices and ( ) . for simplicity , and without loss of generality, we rely only on the first three fields of the 5-tuples in this paper i.e. , which describe the initiation of contact events .we refer to these 3-tuples simply as the `` contact tuples '' from this point onwards .the contact duration is not considered here due to the lack of explicit session termination in the dataset , which creates a degree of uncertainty around the exact timing of session completion . though this uncertainty is limited to the order of minutes, the incorporation of this uncertainty into the shuffling approach is out of scope of this paper and is left for future work .   as a preamble to our main inducement shuffling results ,we apply the pre - existing contact - shuffled null models presented by the authors in `` small but slow world ''  to our originally inferred contact network .this allows us to compare and contrast spreading behavior against that observed in prior work .we refer to these earlier null models simply as the `` sbsw '' or `` contact - shuffled '' null models .the sbsw models were previously applied to a number of contact networks , most notably a large mobile call network ( mcn ) with timestamped links between caller / callee pairs .the authors use strings of capital letter abbreviations in naming the contact - shuffled null models , where each letter represents a retained correlation .these correlations are ( d)aily pattern i.e. overall event frequency , ( c)ommunity structure , ( w)eight topology correlation ( b)ursty event dynamics on single links and ( e)vent - event correlations between links . belowwe reproduce verbatim the description of the sbsw null models , more details about which can be found in the original paper :  * dcwb ( _ equal - weight link - sequence shuffled _ ) : whole single - link event sequences are randomly exchanged between links having the same number of events .temporal correlations between links are destroyed .* dcb ( _ link - sequence shuffled _ ) : whole single - link event sequences are randomly exchanged between randomly chosen links .event - event and weight - topology correlations are destroyed .* dcw ( _ time - shuffled _ ) : time stamps of the whole original event sequence are randomly reshuffled .temporal correlations are destroyed .* d ( _ configuration model _ ) : the original aggregated network is rewired according to the configuration model , where the degree distribution of the nodes and connectedness are maintained but the topology is uncorrelated .then , original single - link event sequences are randomly placed on the links , and time shuffling as above is performed .all correlations except seasonalities like the daily cycle are destroyed .our main results are based around the inducement - shuffled null models presented below which are framed in terms of ( t)imes , ( l)ocations and ( n)odes . the input to our inducement models are the session tuples .the output is a set of new session tuples of equal length with one or more of the correlations between pairs of t , l and n destroyed .we perform contact inference on the output sessions using the method just described to arrive at a set of new contact tuples .we reiterate that because inducement shuffling results in a different set of colocation events : it _ implicitly _ induces a modified contact network during contact inference , rather than explicitly reconfiguring the contact network itself .the listing below describes each of the new inducement null models .each model s abbreviation is based on paired capital letters which indicate the retained correlation(s ) between times , locations and nodes .for example , the null model ln - tn retains ( l)ocation/(n)ode and ( t)ime/(n)ode correlations .this means that , compared to the original traces , individual nodes still visit the same locations and they initiate sessions at the same start times .the change from the original trace is shuffling individual sessions relative to locations , thereby destroying the correlation between locations and times .similarly , ln retains only ( l)ocation/(n)ode correlation . under this notation , the original session trace could also be referred to as ln - tn - tl as correlations are retained between all pairs of location , node and time .note that our inducement models only destroy _ correlations _ between the three variables they do not alter the independent frequency distribution of times , locations and nodes . in other words , nodes , locations and times with frequent activity maintain their activity levels in the shuffled trace. moreover , session _ durations _ are always retained .that is , even if session times are shuffled , pairs of start and end times always move together .the inducement models are summarized in table [ tbl : null_model_summary ] in addition to the detailed listing below .note that the final column of table [ tbl : null_model_summary ] includes spreading prevalence at 1 day , the meaning of which will become clear when we explain spreading dynamics shortly .* ln - tn ( _ maintains the location visitation and session start times of nodes , while destroying correlations between time and location _ ) : sessions are first grouped by node . for each grouping, the list of time pairs are shuffled ( i.e. each start / end pair is exchanged with another pair in the same group ) .grouping by node acts to `` loosely bind '' nodes and times although the times are shuffled , they are always reallocated to the same node and therefore only the binding between times and locations is destroyed .i.e. ln and tn correlations are retained while tl correlation is destroyed .* tl - ln _ maintains the location visitation sequence of nodes and the correlation between time and location , while shuffling the node relation with session start time _ :sessions are first grouped by location . for each grouping ,the list of nodes are shuffled .again , grouping acts as a loose binding mechanism keeping the same location / node association .i.e. tl and ln correlations are retained while tn correlation is destroyed .* ln _ maintains the location visitation sequence of nodes , while destroying the correlation between session times and both locations and nodes _ : time pairs of the entire trace are shuffled .ln correlation is retained while tn and tl correlations are destroyed .* tn _ maintains the session times for nodes , while destroying the correlations between locations and both nodes and session times _ : locations of the entire trace are shuffled .tn correlation is retained while ln and tl correlations are destroyed .* tl _ maintains the correlation between session times and locations , while destroying correlations between nodes and both session times and locations _ : nodes of the entire trace are shuffled .tl correlation is retained while ln and tn correlations are destroyed . *the empty set _ destroys all pairwise correlations between time , location , and nodes , while maintaining the independent frequency distributions of all three variables _ : locations of the entire trace are first shuffled and then nodes of the entire trace are shuffled .all correlations between time , location and node are destroyed .  in totalthere are potential models ( including original ) based on which if any of the correlation pairs chosen from ( ln , tn , tl ) are retained during shuffling ; however we omit one null model tl - tn from our analysis .tl - tn would in theory group by time and shuffle locations in order to destroy only the location / node ( ln ) correlation . unlike location and node however , time is not a categorical variable and so grouping would require a discretization of times into an arbitrary number of slots .it is not readily apparent why one number of slots should be chosen over any other and so we leave contemplating tl - tn for future work .we note that in our trace , locations are inherently discrete individual aps with known identifiers .the inducement - shuffled null models do however generalize to broader settings , provided locations can be discretized .for example , a trace of mobile wireless bluetooth contacts annotated with known gps coordinates might be discretized into a grid of lat / lon squares or geographically clustered . on the other hand , a contact network with no known locations ( e.g. email ) is not amenable to shuffling with the models presented in this paper .moreover , though we focus our own simulations on a contact trace predicated on colocated wireless devices , the theme of times / locations / nodes is generalizable in the context of contact inference .we model spreading atop of all contact networks using the susceptible - infected ( si ) infection model  .nodes in the si model are in one of two states : ( s)usceptible or ( i)nfected . state change is unidirectional with nodes graduating from s to i upon satisfying the infection condition in our trace , colocation of a susceptible and infected device . under the si model, infection prevalence is monotonically nondecreasing as a function of time growing until all devices reachable from initial conditions are infected .similar to the work in  , we start by first infecting a randomly chosen node at a randomly chosen contact event .the chosen event s timestamp is interpreted as the simulation trial start time .we restrict the random sampling of the initial event to the first 4 days of trace to ensure a minimum of 10 days simulation `` runway '' before reaching the end of the trace .this 4/10 partition provides ample sampling opportunity across peak and trough traffic periods as well as weekdays and weekends while allowing enough simulation runway to observe the prevalence growth pattern . after sampling the initial infection event, we discard those contacts that occur either prior to the event or days after the event .this ensures all simulations run exactly 10 days , preventing a non - uniform number of samples beyond the 10-day period ( e.g. only initial infection events sampled from within the first 12 hours of trace would have known prevalence at 13.5 days ) .we proceed to calculate the prevalence denominator as equal to the size of the largest connected component ( lcc ) of the aggregated 10-day contact network which typically consists of the majority of all devices ( ) in the period .note that on rare occasions the initially sampled device will fall outside of the lcc . in this casewe simply resample until the device is a part of the lcc .starting at the initial infection and stepping chronologically through the contact sequence we then simulate the si model of ideal diffusion whereby a susceptible device becomes infected upon contact with an already infected device .we denote the set of infected devices at time as and the infection prevalence at time as .we perform a total of 250 random spreading trials ( different starting nodes ) and average the results . in the supporting material we also provide a comprehensive pairwise comparison of spreading potential for all inducement - shuffled null models along with standard errors around the averaged results .in figure [ fig : sbsw_prev_vs_time_lcc_true ] we present the spreading results under the pre - existing sbsw contact - shuffled null models on the st lucia contact sequence . the pronounced `` wavestep '' pattern here captures the daily cycle of human activity well .we also note that the time to near full prevalence in our trace is on the order of a few days , remarkably shorter than the order ( days ) in mcn  .this is due to the fact that , in a wi - fi network successive transmissions can occur within a short period from one infected node to multiple susceptible nodes that simultaneously connect to the same ap , accelerating the whole spreading process .interestingly , our results show that the diffusion rate in dcwb is substantially faster than in original , whereas dcwb and original have been found to have a nearly identical diffusion rate in mcn  .this suggests that the temporal correlation between contact links is the most substantial impediment to the spreading in the wi - fi network . further destroying link weights ( dcb ) or bursty single - link event sequences ( dcw ) only leads to a slightly faster diffusion .this also significantly differs from the observed effect of the similar null models in mcn , where the diffusion rates follow dcw dcb dcwb .we conjecture that link weights and bursty single - link event sequences make little difference in our trace due to the relative homogeneity of link weights most device contacts occur only once ( table [ tbl : repeat_contacts ] ) .this means destroying weight or bursty event correlations does little to perturb our contact network . by comparison ,the mcn in  we calculate to have average link weight ( calls on only links ) , whereby destruction of link weights or bursty event sequences would lead to substantial perturbation .finally , consistent with  we find d to spread fastest .we note however that the marginal difference is less than observed in the prior work .we now present our main result in figure [ fig : ssr_prev_vs_time_lcc_true]the subsequent rate of spreading as a function of time after inducement shuffling of the session records , which are averaged over trials .the histograms of the prevalence after one day in different trials under each null model are shown in figure [ fig : one_day_prevs_hists ] with the characteristics summarized in table [ tbl : null_model_summary ] .the original trace is found to spread slower than all of the inducement - shuffled null models , indicating the combined effects of location / node , time / node and time / location correlations result in the slowest spreading . in other words ,the intrinsic coupling of movement patterns of the nodes in time and space seem to be impeding spreading by limiting randomness of contacts .destroying the time / location correlation with ln - tn only marginally accelerates spreading and further destroying the location / node correlation in tn produces little further acceleration .this suggests that location - specific movement dynamics , which may attract nodes to some locations and repel them from other , are not the primary impediment to spreading .in contrast , destroying the time / node correlation with tl - ln substantially accelerates spreading . maintaining the location / node correlations while destroying all temporal correlations( ln ) also leads to relatively quick spreading , which provides further support that time / node correlations are responsible for slow spreading . though it is interesting that some crossover is observed around 25 days between tl - ln and ln , there is little statistical strength to the statement that ln is ever truly faster which is made clear by comparing tl - ln and ln in figure [ fig : ssr_prev_delta_sem_pairs_lcc_true_abs_lim ] ( supporting information ) .tl and occupy the top echelon with respect to speed of spreading .this indicates two things : ( i ) location / node correlations have some impeding effect on spreading ( tl being faster than tl - ln ) and ( ii ) although tl produces more contacts than by keeping the correlation between time and location , both have a similarly fast spreading .the underlying reasons for this similarity will be explored in the next section . in summary, time / node correlation is found to be the main impediment to spreading with location / node correlation playing a smaller role .   to further explore the observed spreading phenomena , we study the contact frequency and its relation with the infection prevalence in each inducement - shuffling null model . in the spreading process under each null model , the infection prevalence at a specific time and the cumulative contact frequency upon that timeare correlated , as they are both a monotonically increasing function of time .a question remains whether the infection prevalence is uniquely determined by the contact frequency across different null models .in other words , does infection prevalence and contact frequency have a direct causality . as we show in the following, there is no simple causality between these two , suggesting that the contact frequency is not sufficient to distinguish the spreading potential in different null models .we begin by characterising the contact and session statistics over time and space in figures [ fig : active_sessions ] through [ fig : contacts_per_node_ecdf_uniq_lcc_true ] .figure [ fig : active_sessions ] shows the number of active sessions over time , clearly showing the differences in session volumes over weekdays and weekends and the diurnal patterns .we expect this to result in higher spreading propensity during weekdays when there are significantly more contacts .figure [ fig : locations_per_node_ecdf_lcc_true ] shows the ecdf of the unique locations visited per node for each of the inducement null models .a clear clustering of 2 sets of null models emerges , where all the models that destroy the location - node correlation ( omit ln from their name ) result in a higher number of unique locations visited by each node .figures [ fig : contacts_per_node_ecdf_total_lcc_true ] and [ fig : contacts_per_node_ecdf_uniq_lcc_true ] compare the total and unique contacts per node , or put another way , the node degrees in the networks based on contacts .the total contacts distribution is comparable for all null models , with slight differences among the models . for unique contacts ,we observe more pronounced differences between the models , where models that destroy ln ( tl , tn , and ) , produce the largest number of unique contact pairs .this effect is likely a result of the greater number of unique locations produced by these null models , which increases the likelihood of new unique contacts .ln produces the second highest number of unique contacts , while preserving any temporal correlation with ln results in fewer yet similar results .the original trace produces the least contacts , confirming that the inherent spatiotemporal node correlations limits unique contact opportunities .the null models also impact the intersession times for each node , as shown in figure [ fig : intersession_time_ecdf_lcc_true ] . a clear separation of two groups of null models emerges between null models that break the node relation with session start time ( omit tn ) , and those that preserve it . all null models that preserve tn have shorter intersession time , as the the temporal correlation between successive sessions is apparent .large spikes in the plot account for typical session renewal times , such as at around 1 second when multiple attempts to establish a session occur , or at 5 , 10 , 15 , and 20 , 25 , and 30 minutes , where access points typically update session status every 5 minutes . for null models that break tn, intersession times are significantly longer , emphasising the contribution of the time - node correlation to shorter intersession times .we turn our attention next to elucidating the total contact counts in figure [ fig : ssr_contact_count_vs_time_total ] .this effectively captures the total number of links in the network over time based on observed contacts , in contrast with the degree distribution shown above that illustrated comparable degree distributions for all null models .all contact tallys exhibit the characteristic diurnal stepping pattern of five weekdays interleaved with two weekend days .original and tl grow at essentially the same rate ( overlapping lines ) as they both retain the correlation between times and locations leading to the same number of total colocation events .we say `` essentially '' rather than `` exactly '' , as all null models which decorrelate time and node ( tl - ln , ln , tl , ) can occasionally produce `` imaginary '' contact events whereby a node is colocated with itself .such events are discarded during contact inference and so are not accounted for in our tallys .for tl we find these imaginary contacts account for a negligible portion of all contact events ( 0.03% ) and so tl appears to overlap original .tl - ln on the other hand clearly illustrates the imaginary event phenomenon .in fact , the delta between original and tl - ln in figure [ fig : ssr_contact_count_vs_time_total ] is a direct measure of the the number of discarded imaginary contacts under tl - ln shuffling which we find typically runs around 3% .it is interesting to note that ln is the only other shuffling with non - negligible imaginary events , again around 3% .the implication is that individual nodes likely have a strong affinity for specific locations ( retained by * ln ) leading to a ( relatively ) high number of imaginary events when the timing of node s presence in the network is shuffled .ln - tn produces the fewest total contacts indicating that correlated times and locations are the largest driver of contact volume in the original trace . further destroying either the location / node or time / node correlation as is done by tn and ln respectivelyincreases total contacts .we expect that tn , ln and all produce the same number of total contacts as they all have the same expected number of nodes at a given location at a given time . the observed disparity of ln having fewer total contacts than tn and is simply attributable to the % of imaginary contacts produced and discarded under ln shuffling .we now focus to the unique contact counts in figure [ fig : ssr_contact_count_vs_time_unique ] .again , all contact tallys exhibit the characteristic diurnal stepping pattern being strongly driven by macro - scale periodic activity in the network . whereas the original trace produces the most total contacts ( in a tie with tl and tl - ln before discarding imaginary contacts ) , it also produces the _ least _ unique contacts .this suggests the `` mixing '' effect of the null models which increases unique contacts tends to be stronger than the opposite hindering effect the null models sometimes have on total contact volume .ln - tn and tl - ln produce approximately the same number of unique contacts which implies that destroying either time / location or time / node correlation has about equal effect on unique contacts .destroying time / location and time / node correlations leaving only location / node correlation ( ln ) further increases unique contact . tn and produce still more unique contacts , possibly because the aforementioned affinity of devices for specific locations which is retained in ln had a stronger impeding effect on new unique contacts than does node s time preferences .tl leads to the most unique contacts , likely because it retains the total contact boost driven by node s preferences to be in the same location at the same time with the added benefit of mixing which nodes partake in the contact event .  as a final point of comparison between figures [ fig : ssr_contact_count_vs_time_total ] and [ fig : ssr_contact_count_vs_time_unique ] we note how unique contacts are always within a factor of 2.5 of total contacts .again referring to table [ tbl : repeat_contacts ] , this is likely a by - product of a contact network whose original link `` weights '' as measured by repeat contact count are quite low versus the mcn analyzed in  ( average link weight ) .already figures [ fig : ssr_contact_count_vs_time_total ] and [ fig : ssr_contact_count_vs_time_unique ] appear to suggest that there is a weak relationship between a null model s propensity to produce contact events and its subsequent spreading potential .we now proceed to plot contacts versus prevalence where this will become even more obvious .   figure [ fig : ssr_prev_vs_contacts_total_lcc_true ] and figure [ fig : ssr_prev_vs_contacts_unique_lcc_true ] plot the infection prevalence as a function of the number of total and unique contacts respectively .it is evident that the relation between the infection prevalence and the contact frequency varies in different null models , suggesting that no direct causality exists .that is to say , the time of reaching a given prevalence in each null model is different , and the number of contact events upon this time is different as well . therefore , without knowing the type of the null model , one is not able to infer the infection prevalence directly from the contact frequency .we can also interpret this phenomenon by using the term `` spreading efficiency '' , i.e. the number of contacts required to reach a specific prevalence .our results demonstrate that the proposed null models have different spreading efficiency .it is interesting to note that this disparity in spreading efficiency has also been implicitly observed both in this paper and prior work  under contact shuffling .this follows from the fact that contact shuffling inherently retains the same total contact frequency as a function of time , even after shuffling .although unique ( non - repeat ) contacts may deviate from the original trace throughout the simulation period under d and dcw shufflings , these also equalize to that of the original trace by the end of the simulation . in any case ,dcwb and dcb which match original in both total and unique contacts at each time step present with drastically superior diffusion potential ( on a per - contact basis ) than the original trace in our analysis .we suggest that future work may wish to further explore the relationship between both the static and temporal structures of contact - shuffled and inducement - shuffled networks .doing so may reveal common emergent properties such as statistical similiarities that offer a unified explanation to the disparity of spreading efficiency .this paper has analyzed impediments and catalysts to spreading in a contact network through the introduction of a set of inducement - shuffled null models which separately destroy the correlations between times , locations and nodes .the inducement - shuffled null models have enabled second - order causal reasoning about the observed spreading propensity .that is , how is spreading affected by the idiosyncratic behavior that lead to the observed contact network in the first place , rather than how the observed contact network alone affects spreading . among our main observationsis that ( i ) spreading is primarily impeded by time / node correlation and ( ii ) though correlations have a slowing effect in general , retaining time / location correlation alone proves an exception which slightly increases the rate of spreading versus a network with all correlations destroyed .furthermore we have demonstrated a curious disparity between a null model s ability to produce frequent contact events and its propensity to promote spreading . finally , we have found that under pre - existing contact - shuffled null models temporal link correlations are the main spreading impediment in our trace , in contrast to earlier reported results .we conclude by proposing a number of avenues for future work .firstly , there are several areas already alluded to in this manuscript . these are ( i ) defining and justifying appropriate grouped shuffling models on non - categorical variables such as time ( ii ) establishing if and how `` imaginary '' contact events between a node and itself ought to ever be avoided in shuffling and ( iii ) clearly articulating the conditions which may lead to large disparities between contact volume and prevalence . more broadly , it would be useful to explore whether the abstraction of times , locations and nodes generalizes well to other data traces of colocation contact networks , and indeed to other types of contact networks , particularly those which do not operate at human scale ( e.g. cellular level networks ) .complex networks in itself offers a unified framework for contemplating a diverse range of systems and so we expect that some subset of these may well be framed in a similar null model construction to that used in this paper .moreover , there may exist alternative null model abstractions that will afford the same second - order causal reasoning about the nature of spreading in other types of contact networks .we urge the reader to consider what these abstractions might be .10 [ 1]`#1 ` urlstyle [ 1]doi:#1  [ 1 ] [ 2 ]  _ _ _ _ _ _ _ _ _ _ _ _ _ _ key : # 1 + annotation : # 2 _ _ _ _ _ _ _ _ _ _ _ _ _ _  albert r , barabsi al ( 2002 ) statistical mechanics of complex networks .rev mod phys 74 : 4797 .newman me ( 2003 ) the structure and function of complex networks .siam review 45 : 167256 .barrat a , barthelemy m , vespignani a ( 2008 ) dynamical processes on complex networks , volume 1 . cambridge university press cambridge .barabsi al , albert r , jeong h ( 2000 ) scale - free characteristics of random networks : the topology of the world - wide web .physica a : statistical mechanics and its applications 281 : 6977 .jeong h , tombor b , albert r , oltvai zn , barabsi al ( 2000 ) the large - scale organization of metabolic networks .nature 407 : 651654 .mason o , verwoerd m ( 2007 ) graph theory and networks in biology .systems biology , iet 1 : 89119 .bullmore e , sporns o ( 2009 ) complex brain networks : graph theoretical analysis of structural and functional systems .nature reviews neuroscience 10 : 186198 .redner s ( 1998 ) how popular is your paper ?an empirical study of the citation distribution .the european physical journal b - condensed matter and complex systems 4 : 131134 .newman me ( 2004 ) coauthorship networks and patterns of scientific collaboration .proceedings of the national academy of sciences 101 : 52005205 .eagle n , pentland as , lazer d ( 2009 ) inferring friendship network structure by using mobile phone data .proceedings of the national academy of sciences 106 : 1527415278 .pastor - satorras r , vespignani a ( 2001 ) epidemic spreading in scale - free networks .physical review letters 86 : 3200 .newman me ( 2002 ) spread of epidemic disease on networks .physical review e 66 : 016128 .holme p , saramki j ( 2012 ) temporal networks .physics reports 519 : 97125 .liu sy , baronchelli a , perra n ( 2013 ) contagion dynamics in time - varying metapopulation networks . physical review e 87 : 032805 .zhao k , stehl j , bianconi g , barrat a ( 2011 ) social network dynamics of face - to - face interactions .physical review e 83 : 056109 .starnini m , baronchelli a , pastor - satorras r ( 2013 ) modeling human dynamics of face - to - face interaction networks .physical review letters 110 : 168701 .aschenbruck n , munjal a , camp t ( 2011 ) trace - based mobility modeling for multi - hop wireless networks .computer communications 34 : 704714 .  eagle n , ( sandy ) pentland a ( 2006 ) reality mining : sensing complex social systems .personal ubiquitous comput 10 : 255268 .hui p , chaintreau a , scott j , gass r , crowcroft j , et al .( 2005 ) pocket switched networks and human mobility in conference environments . in : proceedings of the 2005 acm sigcomm workshop on delay - tolerant networking .acm , wdtn 05 , pp .244251 .su j , chin a , popivanova a , goel a , de lara e ( 2004 ) user mobility for opportunistic ad - hoc networking . in : proceedings of the sixth ieee workshop on mobile computing systems and applications .ieee computer society , wmcsa 04 , pp .hsu wj , helmy a ( 2010 ) on nodal encounter patterns in wireless lan traces .ieee transactions on mobile computing 9 : 15631577 .  thomas b , atkinson i , jurdak r ( 2014 ) content diffusion in wireless manets : the impact of mobility and demand . in : wireless communications and mobile computing conference ( iwcmc ) , 2014 international .. 959966 .johnsort d ( 1994 ) routing in ad hoc networks of mobile hosts . in : mobile computing systems and applications , 1994 .wmcsa 1994 .first workshop on .pp . 158163 .fall k ( 2003 ) a delay - tolerant network architecture for challenged internets . in : proceedings of the 2003 conference on applications , technologies , architectures , and protocols for computer communications .acm , sigcomm 03 , pp .karsai m , kivel m , pan rk , kaski k , kertsz j , et al .( 2011 ) small but slow world : how network topology and burstiness slow down spreading .phys rev e 83 : 025102 .gauvin l , panisson a , cattuto c , barrat a ( 2013 ) activity clocks : spreading dynamics on temporal networks of human contact .scientific reports 3 .anderson rm , may rm ( 1992 ) infectious diseases of humans dynamics and control .oxford university press .as a function of time , for the original contact trace and `` small but slow world '' null model contact shufflings . *each line is based on a uniformly spaced sampling of prevalence over time .note that the sampling resolution of lines is higher than their respective markers , as we only plot every -th marker ( ) to minimize visual clutter .this ( not fitting ) is the reason for nonlinearity between plotted points .the same applies for the other plots presented throughout this paper . ]   as a function of time , for the original contact trace and inducement - shuffled null models . * ]                   as a function of the number of _ total _ contacts , for the original contact trace and inducement - shuffled null models . * ]   as a function of the number of _ unique _ contacts , for the original contact trace and inducement - shuffled null models . * ].null model summary and prevalence at 1 day standard error of the mean . [ cols="<,^,^,^,>",options="header " , ]we include figures [ fig : ssr_prev_delta_sem_pairs_lcc_true ] and [ fig : ssr_prev_delta_sem_pairs_lcc_true_abs_lim ] to enable the interested reader to more closely compare pairwise prevalences under the inducement - shuffled null models .figure [ fig : ssr_prev_delta_sem_pairs_lcc_true ] is designed primarily for macro - scale comparison of prevalences , i.e. approximately how much faster or slower is one shuffle versus another . by comparing specific row and columnsthe reader can easily see any large difference in prevalences as a function of time of a specific pair of shufflings as the y - axis scale encompasses the maximum absolute differences .figure [ fig : ssr_prev_delta_sem_pairs_lcc_true_abs_lim ] on the other hand is designed for micro - scale comparison of prevalences .the y - axis has been zoomed , which hides differences of large magnitude but allows the reader to more clearly visualize standard errors and overlaps between prevalence pairs .this is designed in particular to allow the reader to gauge whether small but perceivable prevalence differences in figure [ fig : ssr_prev_vs_time_lcc_true ] are of much statistical significance .for example , the reader might notice the brief crossover between ln and tl - ln in figure [ fig : ssr_prev_vs_time_lcc_true ] and be curious how significant this result is . by comparing ln and tl - ln in figure [ fig : ssr_prev_delta_sem_pairs_lcc_true_abs_lim ] oneis then able to ascertain that there exists relatively large standard errors around both ln and tl - ln at the time of this measurement and so it is not likely to hold that tl - ln is ever faster than ln with much statistical significance . on the other hand , the reader may be interested in where there are clear differences , such as between tl and ln where there is a substantial amount of space between the two prevalences ( tl being faster ) .  .the y - axis of each subplot is the column label s prevalence subtracted from the row label s prevalence and spans the range interval [ -0.3,0.3 ] i.e. 30  dotted line which is centered at 0.0 .the gray shaded region around each black line ( very small in most plots but visible at high zoom ) is the standard error of the mean of the row label s prevalence .the gray shaded region around the center dotted blue line is the standard error of the mean of the column label s prevalence.,scaledwidth=90.0% ]  , the only difference being that the y - axis range has been zoomed to the interval [ -0.015,0.015 ] i.e. 1.5  side .this highlights the standard error of the mean more clearly and allows one to more easily establish regions of overlap between the reference and comparison s standard errors giving a better idea of where differences are of lower statistical significance.,scaledwidth=90.0% ]

Abstract: temporal contact networks are studied to understand dynamic spreading phenomena such as communicable diseases or information dissemination . to establish how spatiotemporal dynamics of nodes impact spreading potential in colocation contact networks , we propose `` inducement - shuffling '' null models which break one or more correlations between times , locations and nodes . by reconfiguring the time and/or location of each node s presence in the network , these models induce alternative sets of colocation events giving rise to contact networks with varying spreading potential . this enables second - order causal reasoning about how correlations in nodes spatiotemporal preferences not only lead to a given contact network but ultimately influence the network s spreading potential . we find the correlation between nodes and times to be the greatest impediment to spreading , while the correlation between times and locations slightly catalyzes spreading . under each of the presented null models we measure both the number of contacts and infection prevalence as a function of time , with the surprising finding that the two have no direct causality .


in a recent paper ideas were presented which led to the suggestion that the half - lives of alpha emitters , particularly those of lower decay energy , would be strikingly reduced if the activity was in a metallic environment and cooled to temperatures of a few kelvin as compared to ` normal ' decay in insulating materials at room temperature .the authors surmised that , through the influence of the conduction , ` valence ' or ` free ' , electron potential near the nucleus , the alpha decay barrier would be effectively lowered and thus cooling of long - lived radioactive waste might lead to their much more rapid decay and safe disposal .no experimental evidence was offered in support of these suggestions .it is the objective of this paper to report aspects of already published experiments of significance to these suggestions , clearly indicating that the predictions are far from experimental reality .the experiments concern the decay of relatively long lived , and and their daughter decay chains implanted in an iron metal foil and studied at temperatures down to below 20 mk .the original objectives of this work were to study the polarization of the decaying isotopes through measurement of the angular properties of their alpha and gamma emissions - the method of low temperature nuclear orientation ( ltno ) - leading to results on the hyperfine interactions of the isotopes involved , their magnetic dipole moments and the magnetic hyperfine fields they experienced as implants in the ferromagnetic iron lattice .however the results throw direct light upon the suggestions made by kettner et al in ref .brief mention of evidence from experiments involving beta decay is made in the discussion .this paper presents experimental evidence only , without detailed comment on the theoretical considerations on which the proposals of ref . were based .we note however that ( i ) serious objections to the underlying ideas on the effect of screening on alpha particle coulomb barrier penetration have been raised elsewhere and ( ii ) that the suggestion that cooling to low temperatures might be worthwhile depends upon treating conduction electrons as classical gas with mean energy proportional to temperature t. furthermore , the idea that screening can take place by electrons at a debye radius much smaller than the k - shell mean radius , falling towards nuclear radii at and below 1k , contravenes basic quantum mechanics .there are simply no states available to construct such confined electron wavefunctions .if there were they would be occupied by the atomic electrons .more comments are given in the discussion .the experiments which provide the evidence given here were performed at isolde , cern and oxford over a period of several years .other ltno groups , in particular those from leuven and bonn , have published work on implanted alpha emitters cooled to millikelvin temperatures in metals , containing similar evidence ( see e.g. and references therein ) .the basic ideas of the proposed enhancement mechanism are given in sec .[ sec : basid ] , which is followed in sec .[ sec : ltno ] by a survey of the ways in which low temperature nuclear orientation experiments are sensitive to source lifetime and decay correction .[ sec : impl ] gives details of the preparation of the implanted metallic samples used in the work referred to and sec .[ sec : pred ] introduces model calculations based on three possible scenarios regarding the correct lifetimes to use in analysis of the experiments .[ sec : expbeh ] gives an extended analysis of predictions and experimental results for the three decay chains headed by , and .discussion and conclusions are presented in sec .[ sec : discon ] .from ref .  the enhancement of alpha decay rates in a metalis associated with the presence around the metallic ion of a screening charge , due to free electrons , which is taken to reduce the barrier height by the screening energy u . according to this picture, the reduced barrier height enhances the rate of alpha tunneling through the barrier to separate from its parent nucleus , thus reducing the lifetime .since ionic charge screening by free electrons occurs only in metals , it is predicted that large differences of alpha decay lifetime will be observed depending upon whether the decay takes place in an insulator or a metal .an expression is given for u in terms of the charges of the alpha particle z and the daughter nucleus z , the temperature of the lattice electrons and a parameter u(d+d ) which relates to a fusion reaction in a metal : where is the absolute temperature of the metal in which the decay takes place .a ` typical ' value of u(d+d) is given to be 300 ev at 290 kelvin .the temperature dependence arises from taking the drude model for the ` quasi - free ' valence electrons as having an ( average ) kinetic energy of 0.5 kt .based on this expression it is suggested that by cooling the activity in a metal sample to liquid helium temperature ( 4.2 k ) , the half - life of can be reduced from 138 d to 0.5 d and of from 1600 y to 1.3 y , factors of order 1000 , in each case through a reduction of the effective barrier potential by about 420 kev ( see ref . ) .  the phenomenon of ionic charge screening in metals is well established and its consequence is giving rise to small energy shifts , of order several hundred electronvolts , for cross sections in low energy reaction studies in metallic targets , is fully documented in ref . and other sources .the issue in this paper is to explore whether , through a strong dependence of the effect on temperature , charge screening can lead to dramatic consequences at temperatures of order a few degrees and below .three scenarios are considered and their consequences compared with existing experimental evidence .they are :  * the full effect : the suggested mechanism operates fully at all temperatures . * the partial effect : an attenuated version of the mechanism occurs , leading to a 5% reduction in all alpha decay half - lives at 1 k , which however obeys the predicted u temperature dependence . *the null effect : all effects of screenimg on half - life are negligibly small so that ` normal ' half - lives may be used .low temperature nuclear orientation experiments involve cooling radioactive isotopes in samples in which they experience strong hyperfine interactions to temperatures at which they become , in the case of a magnetic interaction , polarised along the direction of the magnetic field .the appropriate temperature range is typically between 1 and 100 mk for activities in , for example , a ferromagnetic iron foil sample . forrelatively long - lived activities such as are concerned here , the experiments are performed with the sample soldered to the cold finger of a dilution refrigerator and involve initial cooling , by stages , to liquid nitrogen ( 77 k ) and liquid helium ( 4.2 k ) temperatures , each for about 24 hours to allow for cooling and establishment of good vacuum conditions ( less then 10 mbar ) , before reaching 1 k attached to a pumped liquid helium reservoir . at1 k temperature the nuclei remain unoriented and ` warm ' counts , to be used for normalisation of the measured anisotropies at lower temperatures , are taken for several hours .circulation of the / mixture in the refrigerator is started and after a few hours the sample temperature enters the millikelvin range .it can be kept there for many days , but often circulation is stopped to allow return to 1 k to take more ` warm ' counts in order that the decay of the sample can be fully allowed for in analysis . in the orientation measurements themselves the basic observable is the anisotropy of angular distribution of emission of particles or radioation from an oriented source where is the angular distribution function at angle with respect to the axis of orientation and temperature .it is derived form experimental count rates by  and are decay and dead - time corrected count rates in a detector when the source in ` cold ' ( oriented at millikelvin temperature ) and ` warm ' ( unoriented at 1 k or above ) , respectively .the decay correction , fundamental to these measurements , is directly relevant to the present work , as it involves the decay constant of a isotope in question through a correction factor where =ln(2)/t is the decay constant , is the real time of the counting period and is the difference between the arbitrary normalisation time and the start of the measurement .after this correction is applied , each count rate can be compared to rates in spectra taken at different times as though they were taken at the same instant in time .physical parameters are extracted from measured anisotropies by comparison of the experimental angular distribution and the theoretical expression where b , u and a are the usual orientation , deorientation and angular distribution coefficients , q are the detector solid angle corrections , p are legendre polynomial and is the fraction in good sites . depending on the nature of a particular experiment , selected information contained in one of the coefficients can be obtained by such a comparison , assuming all the other coefficients are known . inthe work referred to in this paper , the orientation coefficients b , dependent on the product of magnetic dipole moment and the hyperfine field acting on the studied nuclei in the sample , were used to extract the magnetic dipole moment of oriented states and compare them with either the same moments obtained by a different technique or with systematics and theory .it is obvious that should the experimental anisotropy be determined incorrectly , i.e. if the correction for the radioactive decay , made by using decay constants known at room temperature , would not apply at temperatures of 1 k and lower , the extracted magnetic dipole moment would be wrong .additional sensitivity to the appropriateness of the decay correction arises from other detailed properties of the measured anisotropic distributions .the first sensitive feature is that , at the lowest temperatures , the anisotropy must become independent of temperature as the nuclei become fully polarized . since there is a time sequence in such measurements as the sample temperatureis changed , any incorrectness in the source decay correction will impose a false slope or scatter upon the extracted temperature dependence .the second sensitive feature is that the anisotropy involves an increase in observed intensity in some directions to the orientation axis , and in others a decrease , the actual quantitative changes being determined by well established theory of the distribution .the application of an incorrect adjustment for source decay will falsify the relationship between observations in detectors in different directions to the axis .thus , if the decay correction assumes too short a lifetime , the ` warm ' unoriented distribution will be taken to fall too fast , so that any observed increase in intensity , measured at a time later than the ` warm ' distribution , will be analysed as too large relative to its true value by a certain factor , and any simultaneously observed decrease would be analysed as smaller than its true value , by the same factor . these failures would lead to distortion of the relation between the analysed anisotropies in the two directions , which can usually be readily identified .a separate aspect of the ltno technique with relevance to lifetime is the fact that for the observed anisotropies to be characteristic of the hyperfine interaction in a specific nuclear state , usually a ground state , the lifetime of that state must be long enough for the nuclei to reach thermal equilibrium with the metallic lattice and achieve a degree of polarisation characteristic of that temperature and interaction strength .the time for this to be reached , the nuclear spin - lattice relaxation time , t , has been established in implanted , diffused and co - melted metallic samples as following the korringa conduction electron mechanism . in iron samples of the type discussed in this paper t s have been measured to range from many hours to below 100 ms at millikelvin temperatures .the relevant parameter is the ratio t t .there is abundant evidence that were a lifetime to become shorter than 0.1 ms thermal equilibrium will not be achieved . in situations involving a decay cascade , such asare described in this paper , a degree of polarisation may be inherited from a precursor state higher in the decay chain .reference to situations of this kind are made in the text where relevant , as the degree of equilibration will be affected if lifetimes were to be severely reduced on cooling .finally , as a matter of course , olno experiments include measurement of the unoriented intensity at both the start and the end of the experiment , and quite often also at an intermediate time , when the temperature is at close to 1 k. it is a standard requirement that these normalisation measurements must , after due correction for decay of the source , yield a consistent value for the reference ` warm ' intensity to be used in evaluation of all measured anisotropies .if the normalisation should not be consistent this would be immediately apparent and present a challenge to the experimenters .thus we have , in effect , a measure of the source decay at 1 k over the period of the experiment , which is typically at least several days .each experiment has individual sensitivity to sample half - life and the cases of the three alpha decay chains described here are discussed in detail in sec .[ sec : expbeh ] .for the experiments described here , alpha active samples of , and were prepared at the isolde isotope separator facility , cern , the parent activities being implanted at 60 kev into prepared 99.999% pure iron foils which have been carefully surface polished .the implant dose was for mass a= 225 and a=227 and for mass a=224 .experience of implantation of a wide range of elements has shown that the implantation energy , 60 kev , is amply sufficient to allow the implanted ions to penetrate the omnipresent thin oxide layer on the foil surface and come to rest in undisturbed pure iron .estimates based on calculated projected ranges show that an ion with a nucleus of mass a accelerated through 60 kev will penetrate nanometers , or about 75 atomic layers in iron . allowing for an oxide layer of approximately 5 nanometers average depth of the initially implanted alpha emitters is atomic layers of pure iron . in samples where there is an alpha decay cascade ,recoil following alpha emission alters the initial depth distribution .the kev nuclear recoil energy can cause ejection of the daughter from the sample , but , on average , the mean implant depth of those nuclei remaining in the pure iron , about 75% of the initial quantity after a three - stage cascade , is increased considerably compared with the initial depth .many experiments have demonstrated that this implantation energy is adequate to describe the environment of the implants as fully typical of the metal . in the context of low temperature nuclear orientation evidencecomes from the fact that nuclear magnetic resonance ( nmr ) of the implants has been observed at the same frequencies in implanted samples as in samples prepared by thermal diffusion to depths of micron .additional evidence of the implants being in true metallic lattice is the fact that the implanted nuclei have been observed to relax in on - line implantation experiments with time constants t described fully by the korringa conduction electron mechanism .as mentioned is sec . [sec : basid ] we consider detailed estimates of effects of proposed lifetime reductions in three possible scenarios to be referred to as the full , partial , and null cases . in all casesthe lifetime reduction estimates , based on the expression for the potential u , as given in ref . and quoted above , can be readily estimated , without detailed calculation , by taking the systematic half - lives of allowed alpha emitters versus decay energy ( see e.g. ) to obtain d(log t)/de as a function of the alpha particle decay energy , e .  cccccccc   + parent & normal alpha & alpha & normal & u & half - life & predicted alpha & predicted + nucleus & decay half - life & energy & fraction & ( kev ) & reduction & fraction & decay halflife +  & at 290 k * & ( kev ) & ( % ) at 290 k & & factor at 1k & ( % ) at 1k * * & ( % ) at 1k * * * +   + parent & normal alpha & alpha & normal & u & halflife & predicted alpha & predicted + nucleus & decay halflife & energy & fraction & ( kev ) & reduction & fraction & decay halflife +  & at 290 k * & ( kev ) & ( % ) at 290 k & & factor at 1k & ( % ) at 1k * * & ( % ) at 1k * * * +  +  + & 3.66 d & 5686 & 94 & 898 & 6.3 x 10 & & 4.7 s + & & 5449 & 5.5 & 898 & 1.3 x 10 +  + & 55.6 s & 6228 & 100 & 878 & 1.2 x 10 & & 4.7 ms +  + & 0.15 s & 6779 & 100 & 857 & 2.7 x 10 & & 55 x 10 s +  + & 60.6 m & 6090 & 27.2 & 847 & 1.2 x 10 & 26 & 0.82 s + & & 6051 & 69.9 & 847 & 1.3 x 10 & 74 +  +  + & 0.30 x 10 & 8784 & 100 & & +  +  + & 10.0 d & 5830 & 50.7 & 889 & 3.8 x 10 & 46 & 20.6 s + & & 5794 & 24.3 & 889 & 4.3 x 10 & 25 + & & 5732 & 10.1 & 889 & 5.0 x 10 & 12 + & & 5637 & 4.4 & 889 & 6.5 x 10 & 7 +  + & 4.8 m & 6341 & 83.4 & 867 & 7.7 x 10 & 77 & 34 ms + & & 6126 & 15.1 & 867 & 1.3 x 10 & 23 +  + & 32.3 ms & 7067 & 99.9 & 867 & 1.8 x 10 & 100 & 18 x 10 s +  + & 4 x 10 s & 8375 & 99.9 & 857 & 3.3 x 10 & 100 & 1.2 x 10 s +  +  + & x 10 & 4950 & not seen & 898 & 5.0 x 10 & 30% of all & 28 d +  + & 125 m & 6035 & strongest & 878 & 2.0 x 10 & strongest & 0.38 s +  + & & 6537 & & 857 & 4.4 x 10 & 100 & 2 ms +  +  + & 38 h & 5869 & 93 & 847 & 2.1x 10 & 85 & 5.9s + & & 5549 & 7 & 847 & 4.8 x 10 & 15 +  +  + & 18.72 d & 6038 & 24.5 & 918 & 3.2 x 10 & 19.7 & 40.7 s + & 100% alpha & 5979 & 23.4 & 918 & 3.5x 10 & 20.5 + & & 5756 & 20.3 & 918 & 6.8 x 10 & 34.7 + & & 5713 & 4.9 & 918 & 7.6 x 10 & 9.3 + & & 5709 & 8.2 & 918 & 7.6 x 10 & 15.6 +  + & 11.44 d & 5748 & 9.1 & 898 & 5.4 x 10 & 7 & 14.0 s + & 100% alpha & 5717 & 53.7 & 898 & 6.1 x 10 & 46.7 + & & 5607 & 26 & 898 & 7.9 x 10 & 29.1 + & & 5539 & 9.1 & 898 & 9.9 x 10 & 12.7 + & & 5434 & 2.3 & 898 & 13.5 x 10 & 4.4 +  + & 4 s & 6819 & 81 & 878 & 3.1 x 10 & 62.9 & 1.1 ms + & 100% alpha & 6553 & 11.5 & 878 & 5.3 x 10 & 16.6 + & & 6425 & 7.5 & 878 & 7.2 x 10 & 14.7 +  + & 1.8 ms & 7386 & 100 & 857 & 1.0 x 10 & 100 & 1.8 x 10 s +  + & 2.15 m & 6623 & 84 & 847 & 3.3 x 10 & 71 & 33 ms + & & 6279 & 16 & 847 & 7.1 x 10 & 29 +  +  + & 21.77 y & 4950 & 47 & 889 & 5.7 x 10 & 45.4 & 1.00 d + & & 4938 & 40 & 889 & 5.7 x 10 & 38.8 + & & 4870 & 6.1 & 889 & 7.5 x 10 & 7.8 + & & 4853 & 3.7 & 889 & 7.5 x 10 & 4.7 +  + & 21.8 m & 5340 & strongest & 867 & 1.3 x 10 & 100 & 3.4 m +  + & 0.9 m & 6275 & strongest & 867 & 4.0 x 10 & 100 & 13.5 ms +  +  +  +  +  this simple approach is valid as the half - life adjustment relates to the barrier penetration factor , not to the pre - formation of the alpha particle within the parent nucleus .this method , with estimates of u direct from eqn .( [ eq1 ] ) and the typical room temperature value of u(d+d) given in ref . , has been used to obtain estimated half - life reductions , see table [ tab1 ] , for the principal alpha decay transitions involved in the three isotope chains relevant to this paper at 1 k. these are examples of the full scenario .estimates of changes at different temperatures ( 77 k , 4.2 k and 25 mk ) for the full scenario have been made by the same method .for the partial scenario it is assumed that the lifetime change is -5% at 1 k and the simple theory have been used to give the value of u to which this reduced effect would correspond .it has been then further assumed that , to estimate the effects at different temperatures , the temperature dependence follows the predicted t relationship of eqn .the null scenario makes no allowance for any half - life change with temperature .this is the expectation were the screening electrons to obey fermi - dirac statistics and has been used implicitly in all published olno experiments .the decay chains of the three implanted isotopes listed above are shown in figs .[ fig1],[fig5 ] and [ fig8 ] and details of the lifetimes and stronger alpha decay transitions in each decay are given in table [ tab1 ] .all half - lives are taken from .the consequences of the predicted half - life changes are qualitatively different for the three chains as outlined below .   the implanted isotope, is an alpha emitter ( 3.66 d ) and a single sample was studied during an experiment at the nicole dilution refrigerator at isolde , cern , which lasted for about 8 days starting one day after the sample was implanted . the time and temperature sequence of this experiment is shown in fig .[ fig2 ] which also illustrates the predictions based on the full and null scenarios .the null scenario is simple in that , after the first 20 hours or so , all activities are predicted to follow the 3.66 d half - life of the long - lived parent .the full scenario , at the other extreme , predicts that the parent activity , which starts out as the upper line in fig .[ fig2 ] , should show two sharp step increases as the sample is cooled , first to liquid nitrogen temperature , 77 k , then to 4.2 k. at this temperature the predicted half - life is already shorter than the time which elapsed before being cooled further to 1 k , at which the lifetime is predicted to be 4.7 s ( table [ tab1 ] ) so the activity falls away very steeply .the three prominent alpha transitions at 5686 kev ( ) , 6288 kev ( ) and 6779 kev ( ) should thus essentially vanish before the olno experiment started , leaving only the ( temporarily increased ) beta activity , and its daughters , present in the source , with alpha transitions at 6090 kev and 6051 kev , which decay with the normal half - life , 10.6 h.  the ltno experiment has two periods at very low temperature , taken to be for simplicity a steady 25 mk , with periods at 1k at the start , after about 110 hours and at the end , about 190 hours after the sample was made .it is clear that , in the full scenario , the activity should fall steadily throughout the experiment with the a 10.6 h half - life .the partial scenario is illustrated in fig .[ fig3 ] , which compares the predictions of this case with the null scenario . for the partial casethere is little change until the sample reaches 1 k at which there is a small step upward in all decay rates .a much larger step occurs on cooling to 25 mk , immediately in the case of and delayed through the ( unchanged ) 10.6 h beta decay half - life of for the activities of and .the alpha decay fraction of is predicted to increase from its normal value of 36% to 37.2% at 1 k and 43.5% at 25 mk .it is clear from fig .[ fig3 ] that a set of ` warm ' counts taken during the three periods of the experiment with the sample at 1 k would not follow the predictions of the null scenario were the partial scenario to be correct .furthermore large distortions of the ratios of 25 mk activity to 1 k activity in detectors placed at angles for which the true anisotropy would lead to increase / decrease of counts rates would be produced by the common increases predicted on cooling the sample to 25 mk .   in the published experiment on this decay chainonly data the 727 kev gamma transition from the daughter of , , was analysed .[ fig4 ] shows the experimental results which gave anisotropies up to about 7% at the lowest temperatures .the raw data were taken over a period of about 5 days and all decay corrections were made using the simple 3.66 d half - life of .the observed temperature dependence was fitted with the magnetic dipole moment of as the unknown quantity , yielding the value = 0.41(5 ) n.m . , which is in very reasonable agreement with a subsequent laser - based measurement of 0.32(4 ) n.m . . these observations are in complete contradiction to the full scenario prediction that the the activity would follow a 10.6 h lifetime throughout the low temperature experiment .[ fig3 ] shows , on even the partial scenario , the three sets of 1 k ` warm ' counts would have been seriously discrepant , the first and third lying close to the time dependence predicted by the null scenario , but the second being above them by 24% , which was not found , all three sets being in good statistical agreement . a second , equally unobserved , prediction is that the counting rates in all detectors would have been shifted by 36% on cooling to millikelvin temperature . we conclude that the published data provide evidence that any half - life change on cooling to 1k is well below 5% ( the partial scenario assumption ) , less than 1 part in 10 of the full scenario prediction , and that a realistic upper limit of any effect is of order 1% .the same upper limit of 1% applies to any changes between 1 k and 25 mk .the case of the decay chain is basically different since the long - lived parent , normally decays by beta decay with a half - life of 14.8 d to with no alpha branch and is not predicted to show ( major ) half - life change . , with ` normal ' half - life 10.0 d then initiates an alpha decay sequence to .discussion of possible changes in the alpha spectrum caused by changing / branching ratios in this decay chain ( e.g. and ) is omitted as such effects should be much stronger in the decay ( see below ) .  the predicted behaviour on cooling under the three scenarios is illustrated in fig .[ fig6 ] . as shown in the figure ,this sample was the subject of three experiments .the first two took place at isolde , cern , using the nicole dilution refrigerator .of these the first started about 24 hours after the sample was made and continued for about 350 hours whilst the second started after about 750 hours and ended after about 820 hours .the sample was then taken to oxford and the last experiment was run with the sample between about 1300 and 1500 hours old .for each experiment the temperature sequence was similar to the chain experiment described above .  in fig .[ fig6 ] the decay of the parent activity is a straight line with ` normal ' half - life of 14.8 d , whilst the ` normal ' ( 10.0 d ) decay of and its much shorter lived daughters should follow the rising and then falling smooth curve , which is the null scenario prediction for this decay chain .the full scenario prediction is that , in each of the three experiments , the activity , and that of its immediate daughters , should show a large increase to well above the ` normal ' growth curve at 77 k , which disappears over about 30 hours when the sample is held at this temperature . before equilibrium is re - established however , the temperature has been reduced to 4.2 k , leading to a second increase in count rate , which died away within less than hour .the activity then settles into simple equilibrium with the decay of parent , with a 14.8 d half - life .subsequent cooling to 1 k and to millikelvin temperature , and return to 1 k during the experiment , has little effect in this scenario since there is very little activity ` held - up ' in the decay chain for such short daughter half - lives .the beta activity will show similar strong short term increases , which recover with close to its ` normal ' half - life of 45.6 m before also coming to equilibrium with the 14.8 d decay , showing no effect of the intervening activities .it is predicted to decay with a 14.8 d half - life for the duration of the sub-4.2 k periods of all experiments .  after each experiment at low temperature , when the sample is returned to room temperature ,the activities are predicted to fall dramatically then recover towards the null scenario curve .this recovery has the time constant of the ` normal ' 10.0 d half - life and so should take about three weeks , longer than the interval between the first and second experiments .  in fig .[ fig6 ] the partial scenario is seen as producing relatively minor , but still distinctly visible , changes compared to the null scenario .any effect before reaching 1 k is small , but the partial scenario gives a predicted activity increase of 28% in all detectors on cooling between 1 k and 25 mk .   in the first two experiments on this chain only gamma decay data were taken , whilst in the third alpha decay spectra were also observed down to millikelvin temperatures .the published record shows anisotropies measured on the alpha transitions from , on both alpha and gamma transitions from and from the alpha decay of , all precursors of the decay of  .data for the 292 kev gamma transition in the decay of is shown in fig .[ fig7 ] , which gives results for detectors along ( 0 ) and normal to ( 90 ) to the axis of nuclear orientation .the data throughout the decay sequence were treated with decay corrections based on the ` normal ' lifetimes of the longer lived components of the chain, ( 14.8 d ) and ( 10.0 d ) , following the null prediction .several features of all three experiments give clear evidence contrary to the full scenario .the most obvious is that the time dependence of the 1 k ` warm ' counts was in agreement , within small % statistical variation , with the null prediction , in all experiments even though the time variation during each experiment differed depending upon the age of the sample ( see fig .[ fig6 ] ) .secondly , very different temperature dependence was shown for the alpha anisotopies in the decays of ( ` normal ' t= 4.8 m ) and ( ` normal ' t= 32 ms ) .this is only possible , as outlined in sec .[ sec : ltno ] , if there is relaxation of these nuclei to achieve thermal equilibrium with the surrounding metallic iron lattice within their lifetimes .in the full scenario , from table .[ tab1 ] , the lifetimes of and become 34 ms and 18 at 1 k. both become less than 1 at 25 mk , far shorter than the relatively well known korringa mechanism would be able to relax to equilibrium . thus these activities should not become appreciably oriented unless fed from an already oriented source .thus and should both show inherited from the parent .however , has spin 1/2 and for spin 1/2 isotopes no anisotropy is observed in emissions which conserve parity .thus no orientation detected by alpha or gamma decay should be observed in emissions from either or in the full scenario in direct contrast with experiment .  to place an upper limit on any possible effect , predictions of the null and partial scenariosare again compared ( fig .[ fig7 ] ) .the most important feature of the partial scenario is that there is a clear discontinuity in activity as the sample is cooled to 25 mk from 1k which , as detailed above , must distort the 0/90 anisotropy relationship .the data on the 292 kev transition are of high statistical accuracy ( .5% ) and show excellent agreement with theory , having the correct ratio to one another and both tending to a constant value as the temperature approaches 16 mk ( 1/t = 60 k ) . any deviation greater that 2% would be revealed , as compared with the predicted shifts ( which are both upward , i.e to increase the 90 effect and reduce that at 0 ) of % in the partial scenario .the observed anistropies show no sign of such distortions .both alpha and gamma results were analysed to give the magnetic dipole moment of .the value obtained , = 3.89(9 ) n.m . , is in very good agreement with a subsequent laser - based measurement of 3.716(7 ) n.m . .  on this basisthe evidence from the mass chain is that there is no half - life effect above 0.5% .the chain is shown in fig .[ fig7 ] , including predicted changes associated with the full scenario described below .the ` normal ' sequence is by dominant ( 98.6% ) beta decay to , with half - life 21.8 y , followed by the strong alpha sequence     .there is a weak ( 1.4% ) alpha decay branch to , which returns to the main sequence through ( 99% ) beta decay of to .a second weak ( 0.005% ) alpha branch ( 5300 kev ) exists from to which then decays further by dominant alpha decay to .the null scenario prediction is that this decay follows a time dependence basically determined by the time for the two longer - lived alpha decays , ( 18.7 d ) and ( 11.4 d ) , to come into temporal equilibrium with the 21.8 y activity .[ fig9 ] shows that this was complete before the experiment , which took place approximately 150 days after the sample was implanted .both alpha and gamma transitions from all elements of the decay chain were observed and alpha spectra are shown at room temperature ( fig .[ fig10 ] ) and at 1 k and mk ( fig .[ fig11 ] ) .the full scenario estimated half - life changes from table [ tab1 ] alter this sequence fundamentally at 1 k ( and there will be less striking changes at higher temperatures ) . through alpha decay enhancement ,the / branching ratio for is altered from 70 to 1.5 x 10 so decay to should become dominant .furthermore the subsequent decay of also becomes dominated by alpha decay ( 86% ) with beta decay reduced to 14% .thus , as the sample is cooled , not only should the total activity show marked increases but very strong feeding of and should be observed before the source loses activity with a half life of about 1 day , rather than the normal 21.8 y. a further major prediction of the full scenario for this decay chain is that the alpha decay fine structure observed in the decays of and will be seriously altered , the higher energy alpha transitions becoming weaker relative to the lower energy transitions .the calculations presented in table [ tab1 ] predict a doubling at 1 k of the intensity of the 5756 kev transition in the decay of relative to the 6038 kev transition . in relative intensity of the 5434 kev alpha branch should increase from 2.3% to 4.4% whilst the 5717 kev branch is predicted to weaken from 54% to 47% .these combined changes would seriously modify the appearance of the spectral region between 5300 and 6100 kev in the spectrum from this sample at 1 k as compared to room temperature .cooling to millikelvin temperatures would , in this scenario , lead to further major changes in half - life and fine structure relative intensity .the partial scenario predictions for the experiment performed on the decay chain are shown in fig [ fig9 ] .the small change in the / branching ratio has been neglected so that the experiment starts close to the temporal equilibrium situation of the null scenario .cooling to 4.2 k produces .6% increase in all activities , with a further 1.2% increase at 1 k and a much larger ( % ) increase on cooling to 25 mk .these increased activities die away only slowly during the 1 k and 25 mk sections of the experiment , with the exception of which shows a decay with the reduced lifetime of d throughout in this period .this decay is far faster than the null scenario and has direct consequence for the sequence of 1 k ` warm ' counts on alpha transitions from this isotope .   in the data analysis ,all decay corrections were made with the 21.8 y half - life , the null scenario , and are very close to unity . the experimental evidence that the decay chain shows little orno half - life change on cooling has many aspects of which three are considered .the 1 k and mk spectra in fig .[ fig11 ] were taken for equal times .there is clearly no overall change in activity on cooling from 1 k to the lowest temperature , although anisotropy in the transitions is readily seen .+ ( i ) the close similarity of the alpha spectra at room temperature , 1 k and 10 mk , figs .[ fig10 ] , [ fig11 ] shows that the predictions of the full scenario introducing new alpha transitions and eliminating others , did not occur .the , and peaks were predicted to vanish before reaching 1 k. + ( ii ) the observed lack of anisotropy in decay of ( spin 1/2 ) , ( weak hyperfine interaction ) and ( extremely short half - life compared to relaxation time ) are all in agreement with predictions of theory for the reasons cited .these results would be strongly distorted in the partial scenario by the 30% increase in activity on cooling from 1 k to 25 mk .+ ( iii ) the observed large anisotropies of the 6623 kev alpha transition from ( see fig . [ fig12 ] ) have small experimental errors .they show the correct relationship in two directions , 86 and 24 , one requiring increase and the other decrease of the recorded activity , and strong temperature dependence leading to constant maximum values at the lowest temperatures reached . as discussed above for the 292 kev transition in the chain , all these aspects of the data would be disturbed by any increase in activity between 1 k and the lowest temperatures caused by changing lifetime . for this casethe precision of each data point in fig .[ fig12 ] is % .the data were fitted to give the magnetic dipole moment of yielding the value = 3.79(7 ) n.m . in excellent agreement with theoretical prediction .the predicted upward shift of all data in this figure in the partial scenario is close to 30% and would be impossible to miss .thus the limit on half - life change from the mass chain is 1% or lower , based on the lack of activity increase in cooling from 1k to mk , on the constancy of ( normally corrected ) warm counts and detailed evaluation of data on many transitions .the absence of change in the alpha spectrum , although well established qualitatively , places a less stringent limit on possible half - life change since to be clearly observed it requires considerable increase in the alpha decay branching from .in this paper evidence has been presented concerning the prediction that introducing alpha activities into metals and cooling them to temperatures of a few kelvin and below should produce major changes in their decay rates and the appearance of their alpha spectra . on this evidence ,no such changes have been observed with an upper level of one percent , at 1 k , a factor of about 10 smaller than the predicted changes .two of the three nuclear moments deduced from these experiments , which depended upon correct source decay treatment , have been confirmed by independent subsequent measurements ; the third , measured solely by this technique , agrees well with theoretical calculation .the evidence presented has been of five types , namely  1 .consistency of warm counts corrected using normal half - lives - a 1 k property .2 .  absence of activity change between 1 k and millikelvin temperatures as shown by smooth temperature variation of observed anisotropies and the correct low temperature saturation behaviour of strong anisotropies .large effects are predicted , even in the partial scenario .however , these predictons depend upon accepting the t dependence of the screening energy u as applicable down to millikelvin temperature - the original suggestions in ref . made no limit of temperature range and took as their example cooling to 4.2 k. 3 .absence of anisotropy where isotope properties lead to no polarisation .no loss of peaks or appearance of additional peaks in alpha spectra between room temperature and millikelvin temperatures .evidence that ratios of relaxation time to half - life are not changed enough to prevent thermal equilibrium in some shorter lived ground states .types 35 are qualitative rather than quantitative features which , whilst denying the possibility of the full scenario are more difficult to use to place specific limits on much smaller effects .  the emphasis in this paper has been on predictions for alpha decay , not only because the effects suggested are so large , but also because , if confirmed they would have important consequences with regard to long - lived waste disposal .however the same ideas also predict more modest changes in beta decay half lives .the ltno technique has , for more than forty years , studied radioactive samples cooled to sub - kelvin temperatures . since the introduction of methods of cooling of metal samples to millikelvin temperatures in the early 1960 s ,with activity melted , diffused and , more recently , implanted into metals , it has been a routine element of such experiments to correct for decay in the source activity .such corrections have always used the ` normal ' half - life of the isotopes concerned .many tens of different beta - emitting isotopes have been oriented , with lifetimes ranging from many years to a few hours and even less .the host metals used in different studies include the more common iron , cobalt and nickel but also copper , silver , gold and many lanthanides .no evidence for any deviation from the ` normal ' lifetime for these isotopes has been reported by the many research groups involved in this work ( for comprehensive listing see and references therein or search for results on low temperature nuclear orientation ) . although not directly addressed in this paper , a firm upper limit on any lifetime changes associated with cooling beta activities in pure metals can be set at or below 1% .( the well established phenomenon of change in electron capture half - lives with variation of inner electron concentration in different environments is excluded from this remark . )  since ref . appeared there have been several follow - up papers . amongst these the original proponents of the effect , raiola et al . claim to have observed a 6% lifetime decrease on cooling a sample of , implanted into cu , to 12k a result ` consistent in sign but significantly smaller than expected '  ( i.e. 6% compared to 1000% , or 1 part in 150 of the prediction ) .jeppesen et al . report changes in half - life at room temperature between decay of implanted into metals and non - metals of order 0.4% , with comparable errors , where the full prediction would be reduction by a factor ( 1 part in 500 of the prediction ) .the analysis presented in this paper places much more stringent limits on the size of any effect .the upper limit of 1% on any effect at 1 k , compared to predictions of factors above 10 represents 1 part in 10 .the evidence for lack of effect down to 25 mk would , if the proposed theory were simply accepted at all temperatures , place limits lower than 1 part in 10 .one may conclude that the suggestion of alleviating problems associated with the disposal of long - lived radioactive waste by cooling in pure metals is unrealistic .concerns expressed in ref . regarding the reliability of other less topical but scientifically equally important situations where reliance is placed upon the use of ` normal ' half - lives in a metallic environment , are also misplaced .the authors acknowledge support from the nicole and isolde ( cern ) collaborations with preparation of the radioactive samples and assistance with some of the reported experiments .this work was supported by grants from epsrc ( uk ) , and by us doe grants no .de - fg02 - 96er40983 ( ut ) and no . de - fg02 - 94er40834 ( umd ) .99 k. u. kettner , h. w. becker , f. strieder and c. rolfs , j.phys .g32 489 ( 2006 ) .m. lindroos , p. richards , j. blomquist , j. rikovska , n. j. stone , and the nicole and isolde collaborations , hyp .75 , 109 ( 1992 ) .m. lindroos , p. richards , j. rikovska , n. j. stone , i. oliveira , k. nishimura , m. booth and the nicole and isolde collaborations , hyp .75 , 323 ( 1992 ) .d. a. williams , d. a. doran , i. s. grant , m. lindroos , i. s. oliveira , j. rikovska , n. j. stone , m. veskovic and the isolde collaboration , hyp .c1 565 ( 1996 ) .n. t. zinner , nucl.phys .a781 , 81 ( 2007 ) .h. b. jeppesen et al . , eur .j. a32 , 31 ( 2007 ) .j. wouters , n. severijns , j. vanhaverbeke and l. vanneste , j. phys .g : nucl . part .17 , 1673 ( 1991 ) .p. schuurmans et al .24 , 4787 ( 1999 ) .n. severijns et al . , phys .c71 , 044324 ( 2005 ) . low temperature nuclear orientation ( eds .n. j. stone and h. postma ) north holland , amsterdam , 1986 .a. f. burenkov , f. f. komarov , m. a. kumakhov and m. m. temkin , tables of ion implantation spatial distributions , gordon and breach , isbn 2 - 88124 - 071 - 2 .p. herzog , chapter 15 , p.746 in low temperature nuclear orientation ( eds .n. j. stone and h. postma ) north holland , amsterdam , 1986 .d. a. williams , d.phil .thesis , oxford , 1997 .p. herzog , h .-folle , k. freitag , m. reuschenbach and h. u. schmidt , phys.lett .a62 , 245 ( 1977 ) .t. l. shaw and n. j. stone , atomic data nuclear data tables , 42 , 339 ( 1989 ) .k. s. krane , _ introductory nuclear physics _, wiley , 1987 . _ table of isotopes _ , 8 edition , ( eds r. b. firestone , v. s. shirly et al . ) wiley , 1996 . j. kilgallon et al . , phys.lett .b405 , 31 ( 1997 ) .j. blomquist , n. freed and h. o. zetterstrom , phys .18 , 47 ( 1965 ) .h. huyga and a. arima , j. phys .jap . supl .34 , 47 ( 1973 ) .b. limata et al .a28 , 251 ( 2006 ) .f. raiola et al . , eur .j. phys . a doi:10.1140/epja / i2007 - 10012 - 8 , ( 2007 ) .

Abstract: the recent suggestion that dramatic changes may occur in the lifetime of alpha and beta decay when the activity , in a pure metal host , is cooled to a few kelvin , is examined in the light of published low temperature nuclear orientation ( ltno ) experiments on such sources cooled to as low as 25 mk , with emphasis here on alpha decay . in ltno observations are made of the anisotropy of radioactive emissions with respect to an axis of orientation . correction of data for decay of activities in metallic samples held at temperatures at and below 1 kelvin for periods of several days has been a routine element of ltno experiments for many years . no evidence for any change of half - life on cooling , with an upper level of order 1% , has been found , in striking contrast to the predicted changes , for alpha decay , of several orders of magnitude . the proposal that such dramatic changes might alleviate problems of disposal of long - lived radioactive waste is shown to be unrealistic .