Miracle-dz/UniFAR-FTUs huggingface dataset:
Queueing Systems with Some Versions of Limited Processor Sharing Discipline

The paper considers a queueing system with limited processor sharing. No more than n jobs may be served simultaneously. This system may be used for modeling bandwidth sharing in wireless communication systems and processes of service in computer networks. If there are n jobs in the considered queueing system and a new job arrives, then the arriving job is lost or the service of a job is interrupted and this job is lost. We study two rules to choose the job to be lost. In accordance with one of these rules, the job with the shortest remaining length is lost. Relations are obtained between the state probabilities of considered system and the state probabilities of the corresponding unlimited processor sharing system. These relations allows to compute the state probabilities for considered system if the state probabilities for the unlimited processor sharing system are known. In the case of Poisson arrival process, the probability that the server capacity is exhausted is equal to the probability that a job is lost. We have obtained an explicit formulas for the stationary state probabilities and the loss probability for this case. These probabilities are invariant under the job length distribution under the condition that the average value of the length is ﬁxed. The second considered rule is the First Come, First Displaced (FCFD) rule. If the service time is equal to a prescribed constant with probability 1, then the shortest remaining length job loss discipline is equivalent to the FCFD discipline. In the case of arbitrary length distribution, the loss probability for the shortest remaining length job loss discipline is greater than the loss probability for another discipline, and, in particular, the FCFD discipline. Hence we have an upper bound for the loss probability in the system with an arbitrary rule for choosing a job to be lost. We have found that, in the case of FCFD rule and constant service length or in the case of the shortest remaining length job loss, the stationary lost probability in a limited egalitarian processor sharing system can be not monotonically decreasing function of the maximum admissible number of jobs in the system for a ﬁxed arrival rate.
Deep Learning Reproducibility and Explainable AI (XAI)

The nondeterminism of Deep Learning (DL) training algorithms and its influence on the explainability of neural network (NN) models are investigated in this work with the help of image classification examples. To discuss the issue, two convolutional neural networks (CNN) have been trained and their results compared. The comparison serves the exploration of the feasibility of creating deterministic, robust DL models and deterministic explainable artificial intelligence (XAI) in practice. Successes and limitation of all here carried out efforts are described in detail. The source code of the attained deterministic models has been listed in this work. Reproducibility is indexed as a development-phase-component of the Model Governance Framework, proposed by the EU within their excellence in AI approach. Furthermore, reproducibility is a requirement for establishing causality for the interpretation of model results and building of trust towards the overwhelming expansion of AI systems applications. Problems that have to be solved on the way to reproducibility and ways to deal with some of them, are examined in this work.
The Extremely Buried Nucleus of IRAS 17208–0014 Observed at Submillimeter and Near-infrared Wavelengths

The ultraluminous infrared galaxy IRAS 17208−0014 is a late-stage merger that hosts a buried active galactic nucleus (AGN). To investigate its nuclear structure, we performed high-spatial-resolution ( ∼ 0.″04 ∼ 32 pc) Atacama Large Millimeter/submillimeter Array (ALMA) observations in Band 9 (∼450 μm or ∼660 GHz), along with near-infrared AKARI spectroscopy in 2.5–5.0 μm. The Band 9 dust continuum peaks at the AGN location, and toward this position CO(J = 6 − 5) and CS(J = 14 − 13) are detected in absorption. Comparison with nonlocal thermal equilibrium calculations indicates that, within the central beam (r ∼ 20 pc), there exists a concentrated component that is dense (107 cm−3) and warm (>200 K) and has a large column density ( NH2>1023cm−2 ). The AKARI spectrum shows deep and broad CO rovibrational absorption at 4.67 μm. Its band profile is well reproduced with a similarly dense and large column but hotter (∼1000 K) gas. The region observed through absorption in the near-infrared is highly likely in the nuclear direction, as in the submillimeter, but with a narrower beam including a region closer to the nucleus. The central component is considered to possess a hot structure where vibrationally excited HCN emission originates. The most plausible heating source for the gas is X-rays from the AGN. The AKARI spectrum does not show other AGN signs in 2.5–4 μm, but this absence may be usual for AGNs buried in a hot mid-infrared core. Further, based on our ALMA observations, we relate the various nuclear structures of IRAS 17208−0014 that have been proposed in the literature.
Network community detection and clustering with random walks

We present a novel approach to partitioning network nodes into non-overlapping communities – a key step in revealing network modularity and hierarchical organization. Our methodology, applicable to networks with both weighted and unweighted symmetric edges, uses random walks to explore neighboring nodes in the same community. The walk-likelihood algorithm (WLA) produces an optimal partition of network nodes into a given number of communities. The walk-likelihood community finder (WLCF) employs WLA to predict both the optimal number of communities and the corresponding network partition. We have extensively benchmarked both algorithms, finding that they outperform or match other methods in terms of the modularity of predicted partitions and the number of links between communities. Making use of the computational efficiency of our approach, we investigated a large-scale map of roads and intersections in the state of Colorado. Our clustering yielded geographically sensible boundaries between neighboring communities.
Fully on-chip microwave photonics system

Microwave photonics (MWP), harnessing the tremendous bandwidth of light to generate, process and measure wideband microwave signals, are poised to spark a new revolution for the information and communication fields. Within the past decade, new opportunity for MWP has emerged driven by the advances of integrated photonics. However, despite significant progress made in terms of integration level, a fully on-chip MWP functional system comprising all the necessary photonic and electronic components, is yet to be demonstrated. Here, we break the status quo and provide a complete on-chip solution for MWP system, by exploiting hybrid integration of indium phosphide, silicon photonics and complementary metal-oxide-semiconductor (CMOS) electronics platforms. Applying this hybrid integration methodology, a fully chip-based MWP microwave instantaneous frequency measurement (IFM) system is experimentally demonstrated. The unprecedented integration level brings great promotion to the compactness, reliability, and performances of the overall MWP IFM system, including a wide frequency measurement range (2-34 GHz), ultralow estimation errors (10.85 MHz) and a fast response speed (∼0.3 ns). Furthermore, we deploy the chip-scale MWP IFM system into realistic application tasks, where diverse microwave signals with rapid-varying frequencies at X-band (8-12 GHz) are accurately identified in real-time. This demonstration marks a milestone for the development of integrated MWP, by providing the technology basis for the miniaturization and massive implementations of various MWP functional systems.
Branching Brownian motion in a periodic environment and uniqueness of pulsating traveling waves

Abstract Using one-dimensional branching Brownian motion in a periodic environment, we give probabilistic proofs of the asymptotics and uniqueness of pulsating traveling waves of the Fisher–Kolmogorov–Petrovskii–Piskounov (F-KPP) equation in a periodic environment. This paper is a sequel to ‘Branching Brownian motion in a periodic environment and existence of pulsating travelling waves’ (Ren et al., 2022), in which we proved the existence of the pulsating traveling waves in the supercritical and critical cases, using the limits of the additive and derivative martingales of branching Brownian motion in a periodic environment.
The mean and variance of the distribution of shortest path lengths of random regular graphs

The distribution of shortest path lengths (DSPL) of random networks provides useful information on their large scale structure. In the special case of random regular graphs (RRGs), which consist of N nodes of degree c ⩾ 3, the DSPL, denoted by P(L = ℓ), follows a discrete Gompertz distribution. Using the discrete Laplace transform we derive a closed-form (CF) expression for the moment generating function of the DSPL of RRGs. From the moment generating function we obtain CF expressions for the mean and variance of the DSPL. More specifically, we find that the mean distance between pairs of distinct nodes is given by ⟨L⟩=lnNln(c−1)+12−lnc−ln(c−2)+γln(c−1)+OlnNN , where γ is the Euler–Mascheroni constant. While the leading term is known, this result includes a novel correction term, which yields very good agreement with the results obtained from direct numerical evaluation of ⟨L⟩ via the tail-sum formula and with the results obtained from computer simulations. However, it does not account for an oscillatory behavior of ⟨L⟩ as a function of c or N. These oscillations are negligible in sparse networks but detectable in dense networks. We also derive an expression for the variance Var(L) of the DSPL, which captures the overall dependence of the variance on c but does not account for the oscillations. The oscillations are due to the discrete nature of the shell structure around a random node. They reflect the profile of the filling of new shells as N is increased. The results for the mean and variance are compared to the corresponding results obtained in other types of random networks. The relation between the mean distance and the diameter is discussed.
Multi-dimensional microwave sensing using graphene waveguides

This paper presents an electrolytically gated broad-band microwave sensor where atomically-thin graphene layers are integrated into coplanar waveguides and coupled with mi-crofluidic channels. The interaction between a solution under test and the graphene surface causes material and concentration-specific modifications of graphene's DC and AC conductivity. Moreover, wave propagation in the waveguide is modified by the dielectric properties of materials in its close proximity via the fringe field, resulting in a combined sensing mechanism leading to an enhanced S-parameter response compared to metallic microwave sensors. The possibility of further controlling the graphene conductivity via an electrolytic gate enables a new, multi-dimensional approach merging chemical field-effect sensing and microwave measurement methods. By controlling and synchronising frequency sweeps, electrochemical gating and liquid flow in the microfluidic channel, we generate multi-dimensional datasets that enable a thorough investigation of the solution under study. As proof of concept, we functionalise the graphene surface in order to identify specific single-stranded DNA sequences dispersed in phosphate buffered saline solution. We achieve a limit of detection concentration of ~ 1 attomole per litre for a perfect match DNA strand and a sensitivity of ~3 dB/decade for sub-pM concentrations. These results show that our devices represent a new and accurate metrological tool for chemical and biological sensing.
A Complete Criterion for Value of Information in Soluble Influence Diagrams

Influence diagrams have recently been used to analyse the safety and fairness properties of AI systems. A key building block for this analysis is a graphical criterion for value of information (VoI). This paper establishes the first complete graphical criterion for VoI in influence diagrams with multiple decisions. Along the way, we establish two techniques for proving properties of multi-decision influence diagrams: ID homomorphisms are structure-preserving transformations of influence diagrams, while a Tree of Systems is a collection of paths that captures how information and control can flow in an influence diagram.
Exploiting Side Information for Improved Online Learning Algorithms in Wireless Networks

In wireless networks, the rate achieved depends on factors like level of interference, hardware impairments, and channel gain. Often, instantaneous values of some of these factors can be measured, and they provide useful information about the instantaneous rate achieved. For example, higher interference implies a lower rate. In this work, we treat any such measurable quality that has a non-zero correlation with the rate achieved as side-information and study how it can be exploited to quickly learn the channel that offers higher throughput (reward). When the mean value of the side-information is known, using control variate theory we develop algorithms that require fewer samples to learn the parameters and can improve the learning rate compared to cases where side-information is ignored. Specifically, we incorporate side-information in the classical Upper Confidence Bound (UCB) algorithm and quantify the gain achieved in the regret performance. We show that the gain is proportional to the amount of the correlation between the reward and associated side-information. We discuss in detail various side-information that can be exploited in cognitive radio and air-to-ground communication in $L-$band. We demonstrate that correlation between the reward and side-information is often strong in practice and exploiting it improves the throughput significantly.
A Dimensionality Reduction Method for Finding Least Favorable Priors with a Focus on Bregman Divergence

A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior, under mild conditions, is then known to be minimax. However, finding least favorable distributions can be challenging due to inherent optimization over the space of probability distributions, which is infinite-dimensional. This paper develops a dimensionality reduction method that allows us to move the optimization to a finite-dimensional setting with an explicit bound on the dimension. The benefit of this dimensionality reduction is that it permits the use of popular algorithms such as projected gradient ascent to find least favorable priors. Throughout the paper, in order to make progress on the problem, we restrict ourselves to Bayesian risks induced by a relatively large class of loss functions, namely Bregman divergences.
Refining the state-of-the-art in Machine Translation, optimizing NMT for the JA EN language pair by leveraging personal domain expertise

Documenting the construction of an NMT (Neural Machine Translation) system for En/Ja based on the Transformer architecture leveraging the OpenNMT framework. A systematic exploration of corpora pre-processing, hyperparameter tuning and model architecture is carried out to obtain optimal performance. The system is evaluated using standard auto-evaluation metrics such as BLEU, and my subjective opinion as a Japanese linguist.
Brezis--Kato Type Regularity Results for Higher Order Elliptic Operators

We prove a Brezis–Kato regularity type results for solutions of the higher order nonlinear elliptic equation Lu = g(x, u) in Ω with an elliptic operator L of 2m order with variable coefficients and a Carathéodory function g : Ω×C → C, where Ω ⊂ R is an open set with N > 2m. 1. Notations and Intorduction The aim of this paper is to generalize the Brezis–Kato theorem [3] for higher order elliptic differential operators with variable coefficients. It is intended to make the least assumptions possible concerning the coefficients of the operator so that it can serve for future references. We consider a linear differential operator L = (−1)m ∑ |α|≤2m aα(x)D α with variable complex-valued coefficients defined in an arbitrary open subset Ω of RN . Here for every multi-index α = (α1, . . . , αN ) we set Dα = ∂ |α| ∂x α1 1 . ∂x αN N and ξα = ξ1 1 . ξ αN N , for a vector ξ = (ξ1, . . . , ξN ) . The characteristic form l(x, ξ) of L is defined by l(x, ξ) = ∑ |α|=2m aα(x)ξ α for x ∈ Ω and real vectors ξ. We say that L is strongly elliptic if there exists λ > 0 such that (1.1) Re(l(x, ξ)) ≥ λ|ξ| for x ∈ Ω and all real vectors ξ = (ξ1, . . . , ξN ). We make standing assumptions: (i) all coefficients aα belong to the space L ∞ loc(Ω), (ii) top-order coefficients aα for |α| = 2m are continuous on Ω. We denote by Ck(Ω) (resp. C∞ 0 (Ω)) the class of complex valued functions defined in Ω which has continuous derivatives up to order k (resp. which are smooth and have compact support). We consider Hölder’s spaces Ck,h(Ω) for nonnegative integers k and 0 < h < 1 which consists of all functions u ∈ Ck(Ω) such that Dαu with |α| = k satisfies the (uniform) Hölder condition of exponent h. The symbol W k,p(Ω) for 1 ≤ p < ∞ denotes the Sobolev space of all complex valued u ∈ Lp(Ω) for which all the distributional derivatives Dαu are also in Lp(Ω) for |α| ≤ k. We consider the norm ‖u‖W k,p(Ω) = (∑ |α|≤k ‖D u‖pLp(Ω) )1/p for u ∈ W k,p(Ω). We use the symbol W k,p 0 (B) to denote the closure of C ∞ 0 (Ω) in the W k,p(Ω) norm. The local Sobolev space W k,p loc (Ω) consists of functions u : Ω → C such that u ∈ W k,p(U) for every open subset U ⊂⊂ Ω (the latter means that U is compact and U ⊂ Ω). Similarly, C k,h loc (Ω) consists of u ∈ C k(Ω) such that u ∈ Ck,h(U) for every open U ⊂⊂ Ω. We see with the aid of the partition of unity that a function u : Ω → C belongs to W k,p loc (Ω) if and only if u ∈ W k,p(B) for every ball B ⊂⊂ Ω. 2010 Mathematics Subject Classification. 35B65, 35J30, 35J61, 35G20.
Bounds on the Twin-Width of Product Graphs

Twin-width is a graph width parameter recently introduced by Bonnet, Kim, Thomass\'{e} & Watrigant. Given two graphs $G$ and $H$ and a graph product $\star$, we address the question: is the twin-width of $G\star H$ bounded by a function of the twin-widths of $G$ and $H$ and their maximum degrees? It is known that a bound of this type holds for strong products (Bonnet, Geniet, Kim, Thomass\'{e} & Watrigant; SODA 2021). We show that bounds of the same form hold for Cartesian, tensor/direct, corona, rooted, replacement, and zig-zag products. For the lexicographical product it is known that the twin-width of the product of two graphs is exactly the maximum of the twin-widths of the individual graphs (Bonnet, Kim, Reinald, Thomass\'{e} & Watrigant; IPEC 2021). In contrast, for the modular product we show that no bound can hold. In addition, we provide examples showing many of our bounds are tight, and give improved bounds for certain classes of graphs.
Gene Expression Time Delays in Reaction-Diffusion Systems

Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also greatly affect the behaviour of reaction-diffusion systems. In this dissertation, we explore their effects on Turing pattern mechanisms. By incorporating time delays, modelled as both a fixed parameter and as a continuous distribution, into classical reaction-diffusion systems that exhibit Turing instabilities, we investigate the changing behaviour of these systems. We find that an introduction of increasing time delay increases the time taken for spatially inhomogeneous patterns to stabilise, and the two are related linearly. We also present results to show, through a linear stability analysis, that an increasing time delay can act both to expand or shrink the Turing space of a certain reaction-diffusion mechanism, depending on the placement of time-delayed terms. Significantly, we find that modelling time delays as a continuous distribution has a negligible impact on qualitative or quantitative aspects of the results seen compared with a fixed time delay of the mean of the distribution. These findings serve to highlight the importance of considering gene expression time delays when modelling biological patterning events, as well as requiring a complete understanding of the cellular dynamics before attempting to apply Turing mechanisms to explain biological phenomena. The results also suggest, at least for the distributions considered in this dissertation, that fixed delay and distributed delay models have almost identical dynamics. This allows one to use simpler fixed delay models rather than the more complicated distributed delay variants.
SeqMapPDB: A Standalone Pipeline to Identify Representative Structures of Protein Sequences and Mapping Residue Indices in Real-Time at Proteome Scale

Motivation: 3D structures of proteins provide rich information for understanding their biochemical roles. Identifying the representative protein structures for protein sequences is essential for analysis of proteins at proteome scale. However, there are technical difficulties in identifying the representative structure of a given protein sequence and providing accurate mapping of residue indices. Existing databases of mapping between structures and sequences are usually static that are not suitable for studying proteomes with frequent gene model revisions. They often do not provide reliable and consistent representative structures that maximizes sequence coverage. Furthermore, proteins isomers are usually not properly resolved. Results: To overcome these difficulties, we have developed a computational pipeline called SeqMapPDB to provide high-quality representative PDB structures of given sequences. It provides mapping to structures that fully cover the sequences when available, or to the set of partial non-overlapping structural domains that maximally cover the query sequence. The residue indices are accurate mapped and isomeric proteins are resolved. SeqMapPDB is efficient and can rapidly carry out proteome-wide mapping to the selected version of reference genomes in real-time. Furthermore, SeqMapPDB provides the flexibility of a stand-alone pipeline for large scale mapping of in-house sequence and structure data. Availability: Our method is available at https://bitbucket.org/lianglabuic/seqmappdb with GNU GPL license.