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Effective and reliable data retrieval is critical for the feasibility of DNA storage, and the development of random access efficiency plays a key role in its practicality and reliability. In this paper, we study the Random Access Problem, which asks to compute the expected number of samples one needs in order to recover an information strand. Unlike previous work, we took a geometric approach to the problem, aiming to understand which geometric structures lead to codes that perform well in terms of reducing the random access expectation (Balanced Quasi-Arcs). As a consequence, two main results are obtained. The first is a construction for $k=3$ that outperforms previous constructions aiming to reduce the random access expectation. The second, exploiting a result from [1], is the proof of a conjecture from [2] for rate $1/2$ codes in any dimension.

Death among subjects is common in observational studies evaluating the causal effects of interventions among geriatric or severely ill patients. High mortality rates complicate the comparison of the prevalence of adverse events (AEs) between interventions. This problem is often referred to as outcome "truncation" by death. A possible solution is to estimate the survivor average causal effect (SACE), an estimand that evaluates the effects of interventions among those who would have survived under both treatment assignments. However, because the SACE does not include subjects who would have died under one or both arms, it does not consider the relationship between AEs and death. We propose a Bayesian method which imputes the unobserved mortality and AE outcomes for each participant under the intervention they did not receive. Using the imputed outcomes we define a composite ordinal outcome for each patient, combining the occurrence of death and the AE in an increasing scale of severity. This allows for the comparison of the effects of the interventions on death and the AE simultaneously among the entire sample. We implement the procedure to analyze the incidence of heart failure among geriatric patients being treated for Type II diabetes with sulfonylureas or dipeptidyl peptidase-4 inhibitors., Comment: For supplemental materials, see https://github.com/AnthonySisti/Adverse-Effects-Estimation-in-Observational-Studies-with-Truncation-by-Death

There are many similarities between the theories of matroids and $q$-matroids. However, when dealing with the direct sum of $q$-matroids many differences arise. Most notably, it has recently been shown that the direct sum of representable $q$-matroids is not necessarily representable. In this work, we focus on the direct sum of uniform $q$-matroids. Using algebraic and geometric tools, together with the notion of cyclic flats of $q$-matroids, we show that this is always representable, by providing a representation over a sufficiently large field.

Twisted bilayer structures have emerged as a fascinating arena in condensed matter thanks to their highly tunable physics. The role of spin-orbit coupling (SOC) in twisted bilayers has gained increasing attention due to its potential for spintronics. Thus, it is appealing to propose new materials for constructing twisted bilayers with substantial SOC. In this work, the intriguing effects induced by twisting two layers of two-dimensional bismuthene are unraveled from large-scale first-principles calculations. We show that spin-orbit coupling significantly affects the electronic properties of twisted bilayer bismuthene, even more than in its untwisted counterpart. We carefully investigate how the interplay between the spin-orbit coupling and the twist angle impacts the band structure and spin textures of twisted bilayer bismuthene. We find that the twist angle can be deemed a control knob to switch from a small-gap semiconductor to a metallic behavior. Most crucially, the accurate analysis of the energy bands close to Fermi energy reveals a twist-tunable splitting in the mexican-hat shape of the bands that can otherwise be obtained only by applying enormous electric fields. Our predictions provide insight into innovative bismuth-based technologies for future spintronic devices., Comment: Unrevised first version of the manuscript

In the present paper we reconsider the integrable case of the Hamiltonian $N$-species Volterra system, as it has been introduced by Vito Volterra in 1937 and significantly enrich the results already published in the ArXiv in 2019 by two of the present authors (M. Scalia and O. Ragnisco). In fact, we present a new approach to the construction of conserved quantities and comment about the solutions of the equations of motion; we display mostly new analytical and numerical results, starting from the classical predator-prey model and arriving at the general $N$-species model, Comment: 24 pages, 9 figures. This paper is a natural prosecution of the work arXiv:1903.03595 and presents different enrichments and enhancements of the results there appeared. In this second version several typos have been corrected

We consider the Lommel functions $s_{\mu,\nu}(z)$ for different values of the parameters $(\mu,\nu)$. We show that if $(\mu,\nu)$ are half integers, then it is possible to describe these functions with an explicit combination of polynomials and trigonometric functions. The polynomials turn out to give Pad\'e approximants for the trigonometric functions. Numerical properties of the zeros of the polynomials are discussed. Also, when $\mu$ is an integer, $s_{\mu,\nu}(z)$ can be written as an integral involving an explicit combination of trigonometric functions. A closed formula for $_2F_1\left(\frac{1}{2}+\nu,\frac{1}{2}-\nu;\mu+\frac{1}{2};\sin(\frac{\theta}{2})^2\right)$ with $\mu$ an integer is given., Comment: 14 pages, two figures, two tables

Let $\mathrm{Sym}_q(m)$ be the space of symmetric matrices in $\mathbb{F}_q^{m\times m}$. A subspace of $\mathrm{Sym}_q(m)$ equipped with the rank distance is called a symmetric rank-metric code. In this paper we study the covering properties of symmetric rank-metric codes. First we characterize symmetric rank-metric codes which are perfect, i.e. that satisfy the equality in the sphere-packing like bound. We show that, despite the rank-metric case, there are non trivial perfect codes. Also, we characterize families of codes which are quasi-perfect.

For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper we will focus on the analogous class of codes within the framework of cyclic subspace codes. Cyclic subspace codes have garnered significant attention, particularly for their applications in random network coding to correct errors and erasures. We investigate one-orbit cyclic subspace codes that are full weight spectrum in this context. Utilizing number theoretical results and combinatorial arguments, we provide a complete classification of full weight spectrum one-orbit cyclic subspace codes.

We present a new application of multi-orbit cyclic subspace codes to construct large optical orthogonal codes, with the aid of the multiplicative structure of finite fields extensions. This approach is different from earlier approaches using combinatorial and additive (character sum) structures of finite fields. Consequently, we immediately obtain new classes of optical orthogonal codes with different parameters.

Misfit layer compounds, heterostructures composed by a regular alternating stacking of rocksalt monochalcogenides bilayers and few-layer transition metal dichalchogenides, are an emergent platform to investigate highly doped transition metal dichalcogenides. Among them, (LaSe)$_{1.14}$(NbSe$_2$)$_2$ displays Ising superconductivity, while the presence of a charge density wave (CDW) in the material is still under debate. Here, by using polarized Raman spectroscopy and first-principles calculations, we show that NbSe$_2$ undergoes a doping-driven collapse of the CDW ordering within the misfit, and no signature of the CDW is detected down to 8~K. We provide a complete experimental and theoretical description of the lattice dynamics of this misfit compound. We show that the vibrational properties are obtained from those of the two subunits, namely the LaSe unit and the NbSe$_2$ bilayer, in the presence of a suitable field-effect doping, and then highlight the 2D nature of the lattice dynamics of NbSe$_2$ within the (LaSe)$_{1.14}$(NbSe$_2$)$_2$ 3D structure., Comment: First version of the manuscript (before revisions)

While programmers know that the low-level memory representation of data structures can have significant effects on performance, compiler support to optimize the layout of those structures is an under-explored field. Prior work has optimized the layout of individual, non-recursive structures without considering how collections of those objects in linked or recursive data structures are laid out. This work introduces Marmoset, a compiler that optimizes the layouts of algebraic datatypes, with a special focus on producing highly optimized, packed data layouts where recursive structures can be traversed with minimal pointer chasing. Marmoset performs an analysis of how a recursive ADT is used across functions to choose a global layout that promotes simple, strided access for that ADT in memory. It does so by building and solving a constraint system to minimize an abstract cost model, yielding a predicted efficient layout for the ADT. Marmoset then builds on top of Gibbon, a prior compiler for packed, mostly-serial representations, to synthesize optimized ADTs. We show experimentally that Marmoset is able to choose optimal layouts across a series of microbenchmarks and case studies, outperforming both Gibbons baseline approach, as well as MLton, a Standard ML compiler that uses traditional pointer-heavy representations.

Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association schemes, strongly regular graphs, and secret sharing schemes. In this paper, we characterize two-weight codes in the rank metric, answering a recent question posed by Pratihar and Randrianarisoa., Comment: Accepted for publication in ISIT 2024

Subspace codes have recently been used for error correction in random network coding. In this work, we focus on one-orbit cyclic subspace codes. If $S$ is an $\mathbb{F}_q$-subspace of $\mathbb{F}_{q^n}$, then the one-orbit cyclic subspace code defined by $S$ is \[ \mathrm{Orb}(S)=\{\alpha S \colon \alpha \in \mathbb{F}_{q^n}^*\}, \]where $\alpha S=\lbrace \alpha s \colon s\in S\rbrace$ for any $\alpha\in \mathbb{F}_{q^n}^*$. Few classification results of subspace codes are known, therefore it is quite natural to initiate a classification of cyclic subspace codes, especially in the light of the recent classification of the isometries for cyclic subspace codes. We consider three-dimensional one-orbit cyclic subspace codes, which are divided into three families: the first one containing only $\mathrm{Orb}(\mathbb{F}_{q^3})$; the second one containing the optimum-distance codes; and the third one whose elements are codes with minimum distance $2$. We study inequivalent codes in the latter two families., Comment: Accepted to the 2024 IEEE International Symposium on Information Theory (ISIT 2024)

Let $18$ only three families of scattered polynomials in $\mathbb F_{q^n}[X]$ are known: $(i)$~monomials of pseudoregulus type, $(ii)$~binomials of Lunardon-Polverino type, and $(iii)$~a family of quadrinomials defined in [1,10] and extended in [8,13]. In this paper we prove that the polynomial $\varphi_{m,q^J}=X^{q^{J(t-1)}}+X^{q^{J(2t-1)}}+m(X^{q^J}-X^{q^{J(t+1)}})\in\mathbb F_{q^{2t}}[X]$, $q$ odd, $t\ge3$ is R-$q^t$-partially scattered for every value of $m\in\mathbb F_{q^t}^*$ and $J$ coprime with $2t$. Moreover, for every $t>4$ and $q>5$ there exist values of $m$ for which $\varphi_{m,q}$ is scattered and new with respect to the polynomials mentioned in $(i)$, $(ii)$ and $(iii)$ above. The related linear sets are of $\Gamma L$-class at least two.

Bonini, Borello and Byrne started the study of saturating linear sets in Desarguesian projective spaces, in connection with the covering problem in the rank metric. In this paper we study \emph{$1$-saturating} linear sets in PG$(2,q^4)$, that is $\mathbb{F}_q$-linear sets in PG$(2,q^4)$ with the property that their secant lines cover the entire plane. By making use of a characterization of generalized Gabidulin codes, we prove that the rank of such a linear set is at least $5$. This answers to a recent question posed by Bartoli, Borello and Marino.

Starting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. The statement of the Second Law is formulated in the classical form and the thermodynamic restrictions are then developed following the Coleman-Noll procedure. However, instead of the Clausius Duhem inequality we consider the corresponding equality where the entropy production rate is prescribed by a non-negative constitutive function. Both the free energy and the entropy production are assumed to depend on a common set of independent variables involving, in addition to temperature, both temperature gradient and heat-flux vector together with their time derivatives. This approach results in rate-type constitutive equations for the heat-flux vector that are intrinsically consistent with the Second Law and easily amenable to analysis. In addition to obtaining already known models (e.g. Cattaneo-Maxwell's, Jeffreys-like and Green-Naghdi's heat conductors), this scheme allows us to build new and more complex models of heat transport that may have applications in describing the thermal behavior in nanosystems. Indeed, when higher order time derivatives of the heat flux vector are involved, many different relaxation times occur within the rate equation., Comment: 32 pages, 2 tables, 1 appendix

In this paper we will study the action of $\mathbb{F}_{q^n}^{2 \times 2}$ on the graph of an $\mathbb{F}_q$-linear function of $\mathbb{F}_{q^n}$ into itself. In particular we will see that, under certain combinatorial assumptions, its stabilizer (together with the sum and product of matrices) is a field. We will also see some examples for which this does not happen. Moreover, we will establish a connection between such a stabilizer and the right idealizer of the rank-metric code defined by the linear function and give some structural results in the case in which the polynomials are partially scattered.

The aim of this paper is to develop a general constitutive scheme within continuum thermodynamics to describe the behavior of heat flow in deformable media. Starting from a classical thermodynamic approach, the rate-type constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. All constitutive functions are required to depend on a common set of independent variables and to be consistent with thermodynamics. The statement of the Second Law is formulated in a general nonlocal form, where the entropy production rate is prescribed by a non-negative constitutive function and the extra entropy flux obeys a no-flow boundary condition. The thermodynamic response is then developed based on Coleman-Noll procedure. In the local formulation, the free energy potential and the rate of entropy production function are assumed to depend on temperature, temperature gradient and heat-flux vector along with their time derivatives. This approach results in rate-type constitutive equations for the heat-flux vector that are intrinsically consistent with the Second Law and easily amenable to analysis. A huge class of linear and nonlinear models of the rate type are recovered (e.g., Cattaneo-Maxwell's, Jeffreys-like, Green-Naghdi's, Quintanilla's and Burgers-like heat conductors). In the (weakly) nonlocal formulation of the second law, both the entropy production rate and an entropy extra-flux vector are assumed to depend on temperature, temperature gradient and heat-flux vector along with their spatial gradients and time derivatives. Within this (classical) thermodynamic framework the nonlocal Guyer-Krumhansl model and some nonlinear generalizations devised by Cimmelli and Sellitto are obtained, Comment: 29 pages

We give different integral representations of the Lommel function $s_{\mu,\nu}(z)$ involving trigonometric and hypergeometric $_2F_1$ functions. By using classical results of Polya, we give the distribution of the zeros of $s_{\mu,\nu}(z)$ for certain regions in the plane $(\mu,\nu)$. Further, thanks to a well known relation between the functions $s_{\mu,\nu}(z)$ and the hypergeometric $ _1F_2$ function, we describe the distribution of the zeros of $_1F_2$ for specific values of its parameters., Comment: 15 pages, 3 figures, 1 Table

The Q&U Bolometric Interferometer for Cosmology (QUBIC) is the first bolometric interferometer designed to measure the primordial B-mode polarization of the Cosmic Microwave Background (CMB). Bolometric interferometry is a novel technique that combines the sensitivity of bolometric detectors with the control of systematic effects that is typical of interferometry, both key features in the quest for the faint signal of the primordial B-modes. A unique feature is the so-called "spectral imaging", i.e., the ability to recover the sky signal in several sub-bands within the physical band during data analysis. This feature provides an in-band spectral resolution of \Delta{\nu}/{\nu} \sim 0.04 that is unattainable by a traditional imager. This is a key tool for controlling the Galactic foregrounds contamination. In this paper, we describe the principles of bolometric interferometry, the current status of the QUBIC experiment and future prospects., Comment: To appear in Proc. of the mm Universe 2023 conference, Grenoble (France), June 2023, published by F. Mayet et al. (Eds), EPJ Web of conferences, EDP Sciences

In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic curve of genus $g$. As well as proving that each such discrete system is an integrable map in the Liouville sense, we also showed it to be an algebraic completely integrable system. In the discrete setting, the latter means that the generic level set of the invariants is an affine part of an abelian variety, in this case the Jacobian of the hyperelliptic curve, and each iteration of the map corresponds to a translation by a fixed vector on the Jacobian. In addition, we demonstrated that, by combining the discrete integrable dynamics with the flow of one of the commuting Hamiltonian vector fields, these maps provide genus $g$ algebro-geometric solutions of the infinite Volterra lattice, which justified naming them Volterra maps, denoted ${\cal V}_g$. The original motivation behind our work was the fact that, in the particular case $g=2$, we could recover an example of an integrable symplectic map in four dimensions found by Gubbiotti, Joshi, Tran and Viallet, who classified birational maps in 4D admitting two invariants (first integrals) with a particular degree structure, by considering recurrences of fourth order with a certain symmetry. Hence, in this particular case, the map ${\cal V}_2$ yields genus two solutions of the Volterra lattice. The purpose of this note is to point out how two of the other 4D integrable maps obtained in the classification of Gubbiotti et al. correspond to genus two solutions of two different forms of the modified Volterra lattice, being related via a Miura-type transformation to the $g=2$ Volterra map ${\cal V}_2$. We dedicate this work to a dear friend and colleague, Decio Levi.

Misfit layer compounds are heterostructures composed of rocksalt units stacked with few layers transition metal dichalcogenides. They host Ising superconductivity, charge density waves and good thermoelectricity. The design of misfits emergent properties is, however, hindered by the lack of a global understanding of the electronic transfer among the constituents. Here, by performing first principles calculations, we unveil the mechanism controlling the charge transfer and demonstrate that rocksalt units are always donor and dichalcogenides acceptors. We show that misfits behave as a periodic arrangement of ultra-tunable field effect transistors where a charging as large as 6\times10^{14} e^-cm^{-2} can be reached and controlled efficiently by the La-Pb alloying in the rocksalt. Finally, we identify a strategy to design emergent superconductivity and demonstrate its applicability in (LaSe)_{1.27}(SnSe_2)_2. Our work paves the way to the design synthesis of misfit compounds with tailored physical properties., Comment: First version of the manuscript (before revisions)

Modern robotics often involves multiple embodied agents operating within a shared environment. Path planning in these cases is considerably more challenging than in single-agent scenarios. Although standard Sampling-based Algorithms (SBAs) can be used to search for solutions in the robots' joint space, this approach quickly becomes computationally intractable as the number of agents increases. To address this issue, we integrate the concept of factorization into sampling-based algorithms, which requires only minimal modifications to existing methods. During the search for a solution we can decouple (i.e., factorize) different subsets of agents into independent lower-dimensional search spaces once we certify that their future solutions will be independent of each other using a factorization heuristic. Consequently, we progressively construct a lean hypergraph where certain (hyper-)edges split the agents to independent subgraphs. In the best case, this approach can reduce the growth in dimensionality of the search space from exponential to linear in the number of agents. On average, fewer samples are needed to find high-quality solutions while preserving the optimality, completeness, and anytime properties of SBAs. We present a general implementation of a factorized SBA, derive an analytical gain in terms of sample complexity for PRM*, and showcase empirical results for RRG., Comment: under review

Sidon spaces have been introduced by Bachoc, Serra and Z\'emor in 2017 as the $q$-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth, Raviv and Tamo in 2018, in which they highlighted the correspondence between Sidon spaces and cyclic subspace codes. Up to now, the known constructions of Sidon Spaces may be divided in three families: the ones contained in the sum of two multiplicative cosets of a fixed subfield of $\mathbb{F}_{q^n}$, the ones contained in the sum of more than two multiplicative cosets of a fixed subfield of $\mathbb{F}_{q^n}$ and finally the ones obtained as the kernel of subspace polynomials. In this paper we will mainly focus on the first class of examples, for which we provide characterization results and we will show some new examples, arising also from some well-known combinatorial objects. Moreover, we will give a quite natural definition of equivalence among Sidon spaces, which relies on the notion of equivalence of cyclic subspace codes and we will discuss about the equivalence of the known examples.

In this paper we extend the study of linear spaces of upper triangular matrices endowed with the flag-rank metric. Such metric spaces are isometric to certain spaces of degenerate flags and have been suggested as suitable framework for network coding. In this setting we provide a Singleton-like bound which relates the parameters of a flag-rank-metric code. This allows us to introduce the family of maximum flag-rank distance codes, that are flag-rank-metric codes meeting the Singleton-like bound with equality. Finally, we provide several constructions of maximum flag-rank distance codes.

The main purpose of this paper is to further study the structure, parameters and constructions of the recently introduced minimal codes in the sum-rank metric. These objects form a bridge between the classical minimal codes in the Hamming metric, the subject of intense research over the past three decades partly because of their cryptographic properties, and the more recent rank-metric minimal codes. We prove some bounds on their parameters, existence results, and, via a tool that we name geometric dual, we manage to construct minimal codes with few weights. A generalization of the celebrated Ashikhmin-Barg condition is proved and used to ensure minimality of certain constructions., Comment: 26 pages

Let $\mathcal{C}\subseteq \mathbb{F}_{q^m}^n$ be an $\mathbb{F}_{q^m}$-linear non-degenerate rank metric code with dimension $k$. In this paper we investigate the problem of determining the number $M(\mathcal{C})$ of codewords in $\mathcal{C}$ with maximum weight, that is $\min\{m,n\}$, and to characterize those with the maximum and the minimum values of $M(\mathcal{C})$.