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Dark matter (DM), in spite of being stable or long-lived on cosmological scales, can decay in the early Universe due to finite-temperature effects. In particular, a first order phase transition (FOPT) in the early Universe can provide a finite window for such decay, guaranteeing DM stability at lower temperatures, consistent with observations. The FOPT can lead to the generation of stochastic gravitational waves (GW) with peak frequencies correlated with DM mass. On the other hand, early DM decay into neutrinos can create a large neutrino asymmetry which can have interesting cosmological consequences in terms of enhanced effective relativistic degrees of freedom $N_{\rm eff}$, providing a solution to the recently observed Helium anomaly among others. Allowing DM decay to occur below sphaleron decoupling temperature, thereby avoiding overproduction of baryon asymmetry, forces the FOPT to occur at sub-electroweak scale. This leaves the stochastic GW within range of experiments like LISA, $\mu$ARES, NANOGrav etc., Comment: 30 pages, 6 captioned figures

This paper considers a novel online fair division problem involving multiple agents in which a learner observes an indivisible item that has to be irrevocably allocated to one of the agents while satisfying a fairness and efficiency constraint. Existing algorithms assume a small number of items with a sufficiently large number of copies, which ensures a good utility estimation for all item-agent pairs. However, such an assumption may not hold in many real-life applications, e.g., an online platform that has a large number of users (items) who only use the platform's service providers (agents) a few times (a few copies of items), which makes it difficult to estimate the utility for all item-agent pairs. To overcome this challenge, we model the online fair division problem using contextual bandits, assuming the utility is an unknown function of the item-agent features. We then propose algorithms for online fair division with sub-linear regret guarantees. Our experimental results also verify the different performance aspects of the proposed algorithms., Comment: We study an online fair division problem that has a large number of items with only a few copies of each item and propose contextual bandits-based algorithms with sub-linear regret guarantees

We consider the problem of fair allocation with subsidy when agents have weighted entitlements. After highlighting several important differences from the unweighted cases, we present several results concerning weighted envy-freeability including general characterizations, algorithms for achieving and testing weighted envy-freeability, lower and upper bounds for worst case subsidy for non-wasteful and envy-freeable allocations, and algorithms for achieving weighted envy-freeability along with other properties., Comment: 20 pages, 1 Table

In this survey we revisit {\sc finite subtraction}, one-heap subtraction games on finite rulesets. The main purpose is to give a general overview of the development, and specifically to draw attention to Flammenkamp's thesis (1997), where he, contrary to other studies, experimentally observes exponential eventual period length of the outcomes, for a carefully selected subclass of games. In addition, we contribute an appendix on {\sc finite excluded subtraction} by Suetsugu., Comment: 15 pages, 2 figures, Appendix by Koki Suetsugu

We propose a novel scenario where thermally under-abundant dark matter (DM) can be revived with a first-order phase transition (FOPT). In the absence of FOPT, thermal DM abundance remains suppressed due to efficient annihilation via mediators. A FOPT brings sharp change to the mass of the mediator at the nucleation temperature such that the final DM relic agrees with observations. We implement this idea in a scenario where DM interacts via a mediator whose initial mass is of same order as DM mass keeping DM annihilation either in allowed or forbidden ballpark. As the mediator mass decreases sharply at the nucleation temperature of the FOPT, the frozen out DM suffers further depletion while keeping final relic within observed limits. DM with sizeable interactions with a light mediator can also give rise to the required self-interactions necessary to solve the small scale structure issues of cold dark matter. While the mechanism is generic to any thermal DM mass, choosing it in the GeV ballpark forces the FOPT to MeV scale which predicts stochastic gravitational waves with nano-Hz frequencies within reach of pulsar timing array (PTA) based experiments like NANOGrav. The existence of light scalar mediator and its mixing with the Higgs keep the scenario verifiable at different particle physics experiments., Comment: 11 pages, 6 captioned figures

We study the possibility of generating dark matter (DM) purely from ultra-light primordial black hole (PBH) evaporation with the latter being produced from a first order phase transition (FOPT) in the early Universe. If such ultra-light PBH leads to an early matter domination, it can give rise to a doubly peaked gravitational wave (GW) spectrum in Hz-kHz ballpark with the low frequency peak generated from PBH density fluctuations being within near future experimental sensitivity. In the sub-dominant PBH regime, the FOPT generated GW spectrum comes within sensitivity due to absence of entropy dilution. In both the regimes, PBH mass from a few kg can be probed by GW experiments like BBO, ET, CE, UDECIGO etc. while DM mass gets restricted to the superheavy ballpark in the PBH dominance case. Apart from distinct DM mass ranges in the two scenarios, GW observations can differentiate by measuring their distinct spectral shapes., Comment: 31 pages, 6 captioned figures, matches version accepted for publication in Phys. Rev. D

We consider an {\em enforce operator} on impartial rulesets similar to the Muller Twist and the comply/constrain operator of Smith and St\u anic\u a, 2002. Applied to the rulesets A and B, on each turn the opponent enforces one of the rulesets and the current player complies, by playing a move in that ruleset. If the outcome table of the enforce variation of A and B is the same as the outcome table of A, then we say that A dominates B. We find necessary and sufficient conditions for this relation. Additionally, we define a {\em selective operator} and explore a distributive-lattice-like structure within applicable rulesets. Lastly, we define nim-values under enforce-rulesets, and establish that the Sprague-Grundy theory continues to hold, along with illustrative examples., Comment: 25 pages, 12 figures, 1 table

Prediction of binding sites for transcription factors is important to understand how they regulate gene expression and how this regulation can be modulated for therapeutic purposes. Although in the past few years there are significant works addressing this issue, there is still space for improvement. In this regard, a transformer based capsule network viz. DNABERT-Cap is proposed in this work to predict transcription factor binding sites mining ChIP-seq datasets. DNABERT-Cap is a bidirectional encoder pre-trained with large number of genomic DNA sequences, empowered with a capsule layer responsible for the final prediction. The proposed model builds a predictor for transcription factor binding sites using the joint optimisation of features encompassing both bidirectional encoder and capsule layer, along with convolutional and bidirectional long-short term memory layers. To evaluate the efficiency of the proposed approach, we use a benchmark ChIP-seq datasets of five cell lines viz. A549, GM12878, Hep-G2, H1-hESC and Hela, available in the ENCODE repository. The results show that the average area under the receiver operating characteristic curve score exceeds 0.91 for all such five cell lines. DNABERT-Cap is also compared with existing state-of-the-art deep learning based predictors viz. DeepARC, DeepTF, CNN-Zeng and DeepBind, and is seen to outperform them.

This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966), with finite subtraction sets. In case of two move rulesets we find a complete solution, via a certain $\mathcal{P}$-to-$\mathcal{P}$ principle (where $\mathcal{P}$ means that the previous player wins). Namely $x \in \mathcal{P}$ if and only if $x +a +b \in \mathcal{P}$, where $a$ and $b$ are the two move options. Flammenkamp 1997 observed that, already in one dimension, rulesets with three moves can be hard to analyze, and still today his related conjecture remains open. Here, we solve instances of rulesets with three moves in two dimensions, and conjecture that they all have regular outcomes. Through several computer visualizations of outcomes of multi-move two-dimensional rulesets, we observe that they tend to partition the game board into periodic mosaics on very few regions/segments, which can depend on the number of moves in a ruleset. For example, we have found a five-move ruleset with an outcome segmentation into six semi-infinite slices. In this spirit, we develop a coloring automaton that generalizes the $\mathcal{P}$-to-$\mathcal{P}$ principle. Given an initial set of colored positions, it quickly paints the $\mathcal{P}$-positions in segments of the game board. Moreover, we prove that two-dimensional rulesets have row/column eventually periodic outcomes. We pose open problems on the generic hardness of two-dimensional rulesets; several regularity conjectures are provided, but we also conjecture that not all rulesets have regular outcomes., Comment: 40 pages, 28 figures. Comments are welcome

Motivated by the recent release of new results from five different pulsar timing array (PTA) experiments claiming to have found compelling evidence for primordial gravitational waves (GW) at nano-Hz frequencies, we study the consequences for two popular beyond the Standard Model (SM) frameworks, where such nano-Hz GW can arise due to annihilating domain walls (DW). Minimal framework of Dirac leptogenesis, as well as left-right symmetric model (LRSM) can lead to formation of DW due to spontaneous breaking of $Z_2$ symmetry. Considering the NANOGrav 15 yr data, we show that the scale of Dirac leptogenesis should be above $10^7$ GeV for conservative choices of Dirac Yukawa couplings with fine-tuning at the level of the SM. The scale of {\it minimal} LRSM is found to be more constrained $M_{\rm LR} \sim 10^6$ GeV in order to fit the NANOGrav 15 yr data. On the other hand, the {\it non-minimal} LRSM can be compatible with the NANOGrav data for $10^2 \, {\rm TeV} \lesssim M_{\rm LR} \lesssim 10^3$ TeV but with the corresponding $B-L$ breaking scale violating collider bounds., Comment: 8 pages, 5 figures, 1 table, version accepted in JCAP

We propose a novel framework where baryon asymmetry of the universe can arise due to forbidden decay of dark matter (DM) enabled by finite-temperature effects in the vicinity of a first order phase transition (FOPT). In order to implement this novel cogenesis mechanism, we consider the extension of the standard model by one scalar doublet $\eta$, three right handed neutrinos (RHN), all odd under an unbroken $Z_2$ symmetry, popularly referred to as the scotogenic model of radiative neutrino mass. While the lightest RHN $N_1$ is the DM candidate and stable at zero temperature, there arises a temperature window prior to the nucleation temperature of the FOPT assisted by $\eta$, where $N_1$ can decay into $\eta$ and leptons generating a non-zero lepton asymmetry which gets converted into baryon asymmetry subsequently by sphalerons. The requirement of successful cogenesis together with a first order electroweak phase transition not only keep the mass spectrum of new particles in sub-TeV ballpark within reach of collider experiments but also leads to observable stochastic gravitational wave spectrum which can be discovered in planned experiments like LISA., Comment: 6+3 pages, 2 captioned figures, matches version accepted for publication in Phys. Rev. D (Letter)

We study the possibility of constraining a scenario with high scale first order phase transition (FOPT) responsible for the cogenesis of baryon and dark matter using gravitational wave (GW) (non)-observations. While the FOPT at high scale is responsible for generating baryon asymmetry through leptogenesis and dark matter via the \textit{mass-gain} mechanism, the resulting GW spectrum falls within the ongoing LIGO-VIRGO experimental sensitivity. The dark matter is preferred to be in the non-thermal ballpark with sub-GeV masses and the criteria of successful dark matter relic rules out a large portion of the parameter space consistent with high scale FOPT and successful leptogenesis. Some part of the parameter space allowed from dark matter and leptogenesis criteria also gives rise to a large signal-to-noise ratio at ongoing experiments and hence can be disfavoured in a conservative way from the non-observation of such stochastic GW background. Future data from ongoing and planned experiments will offer a complementary and indirect probe of the remaining parameter space which is typically outside the reach of any direct experimental probe., Comment: 24 pages, 6 captioned figures, matches version accepted for publication in Phys. Rev. D

We study a scenario where both dark matter and heavy right handed neutrino (RHN) responsible for leptogenesis acquire masses by crossing the relativistic bubble walls formed as a result of a TeV scale supercooled first order phase transition (FOPT). While this leads to a large out-of-equilibrium abundance of right handed neutrino inside the bubble sufficient to produce the required lepton asymmetry, the dark matter being lighter can still remain in equilibrium with its relic being set by subsequent thermal freeze-out. A classical conformal symmetry ensures the origin of mass via FOPT induced by a singlet scalar while also ensuring supercooling leading to enhanced gravitational wave amplitude within the sensitivity of the LISA experiment. A minimal scenario with three RHN, one inert scalar doublet and one singlet scalar as additional fields beyond the standard model is sufficient to realize this possibility which also favours inert RHN dark matter over inert scalar doublet., Comment: 32 pages, 8 captioned figures, matches version accepted for publication in JHEP

We consider a financial network represented at any time instance by a random liability graph which evolves over time. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liability edges. These random edges are modified (locally) by the agents over time, as they learn from their experiences and (possibly imperfect) observations. The settlement of the liabilities of various agents at the end of the contract period (at any time instance) can be expressed as solutions of random fixed point equations. Our first step is to derive the solutions of these equations (asymptotically and one for each time instance), using a recent result on random fixed point equations. The agents, at any time instance, adapt one of the two available strategies, risky or less risky investments, with an aim to maximize their returns. We aim to study the emerging strategies of such replicator dynamics that drives the financial network. We theoretically reduce the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). Using the attractors of the resulting ODE we show that the replicator dynamics converges to one of the two pure evolutionary stable strategies (all risky or all less risky agents); one can have mixed limit only when the observations are imperfect. We verify our theoretical findings using exhaustive Monte Carlo simulations. The dynamics avoid the emergence of the systemic-risk regime (where majority default). However, if all the agents blindly adapt risky strategy it can lead to systemic risk regime., Comment: 37 pages, 3 figures and 4 tables. Accepted for publication in Dynamic Games and Applications. arXiv admin note: text overlap with arXiv:2003.00886

We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional spaces, and our aim is to study their almost-sure solutions. An underlying directed random graph defines the connections between various components of the FP equations. Existence of an edge between nodes $i,j$ implies the $i$-th FP equation depends on the $j$-th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random `neighbour' components. We obtain finite-dimensional limit FP equations in a much smaller dimensional space, whose solutions aid to approximate the solution of FP equations for almost all realizations, as the number of nodes increases. We use Maximum theorem for non-compact sets to prove this convergence. We apply the results to study systemic risk in an example financial network with large number of heterogeneous entities. We utilized the simplified limit system to analyse trends of default probability (probability that an entity fails to clear its liabilities) and expected surplus (expected-revenue after clearing liabilities) with varying degrees of interconnections between two diverse groups. We illustrated the accuracy of the approximation using exhaustive Monte-Carlo simulations. Our approach can be utilized for a variety of financial networks (and others); the developed methodology provides approximate small-dimensional solutions to large-dimensional FP equations that represent the clearing vectors in case of financial networks., Comment: 51 pages, 7 figures and 4 tables, will appear in Annals of Operations Research

The spread of fake news on online social networks (OSNs) has become a matter of concern. These platforms are also used for propagating important authentic information. Thus, there is a need for mitigating fake news without significantly influencing the spread of real news. We leverage users' inherent capabilities of identifying fake news and propose a warning-based control mechanism to curb this spread. Warnings are based on previous users' responses that indicate the authenticity of the news. We use population-size dependent continuous-time multi-type branching processes to describe the spreading under the warning mechanism. We also have new results towards these branching processes. The (time) asymptotic proportions of the individual populations are derived using stochastic approximation tools. Using these, relevant type 1, type 2 performances are derived and an appropriate optimization problem is solved. The proposed mechanism effectively controls fake news, with negligible influence on the propagation of authentic news. We validate performance measures using Monte Carlo simulations on network connections provided by Twitter data., Comment: We revised the paper with 1 additional Theorem. The updated paper has 8 pages, 1 table and 5 figures

We consider a random financial network with a large number of agents. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liabilities. The settlement of the debts of various agents at the end of the contract period can be expressed as solutions of random fixed point equations. Our first step is to derive these solutions (asymptotically), using a recent result on random fixed point equations. We consider a large population in which agents adapt one of the two available strategies, risky or risk-free investments, with an aim to maximize their expected returns (or surplus). We aim to study the emerging strategies when different types of replicator dynamics capture inter-agent interactions. We theoretically reduced the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). We proved that the equilibrium strategies converge almost surely to that of an attractor of the ODE. We also derived the conditions under which a mixed evolutionary stable strategy (ESS) emerges; in these scenarios the replicator dynamics converges to an equilibrium at which the expected returns of both the populations are equal. Further the average dynamics (choices based on large observation sample) always averts systemic risk events (events with large fraction of defaults). We verified through Monte Carlo simulations that the equilibrium suggested by the ODE method indeed represents the limit of the dynamics., Comment: It will appear at the 10th International Conference on NETwork Games, COntrol and OPtimization (NETGCOOP). 19 pages, two figures. In the current version of the paper, many typos are corrected

We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the i th FP equation depends on the j th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random neighbor components. We obtain finite dimensional limit FP equations (in a much smaller dimensional space), whose solutions approximate the solution of the random FP equations for almost all realizations, in the asymptotic limit (number of components increase). Our techniques are different from the traditional mean-field methods, which deal with stochastic FP equations in the space of distributions to describe the stationary distributions of the systems. In contrast our focus is on realization-wise FP solutions. We apply the results to study systemic risk in a large financial heterogeneous network with many small institutions and one big institution, and demonstrate some interesting phenomenon., Comment: 20 pages and 5 figures. In the current version, the Theorem 1 proof is corrected

Many systems require frequent and regular updates of a certain information. These updates have to be transferred regularly from the source to the destination. We consider scenarios in which an old packet becomes completely obsolete, in the presence of a new packet. In this context, if a new packet arrives at the source while it is transferring a packet, one needs to decide the packet to be dropped. New packet has recent information, but might require more time to transfer. Thus it is not clear as to which packet to be dis- carded, and this is the main focus of the paper. Recently introduced performance metrics, called average age of information (AAoI) and peak age of information (PAoI) of the information available at the destination, are the relevant performance measures. These type of systems do not require storage buffers, of size more than one, at the source queue. We consider single source / multiple sources regularly updating information to a single destination possibly over wireless channels to derive optimal drop policies that optimize the AAoI. We showed that the state independent (static) policies like dropping always the old packets or dropping always the new packets is optimal in many scenarios, among an appropriate set of stationary Markov policies. We consider relevant games when multiple sources compete. In many scenarios, the non-cooperative solution almost minimizes the social objective, the sum of AAoIs of all the sources., Comment: 12 pages and 3 figures