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Redback and black widow pulsars are two classes of peculiar binary systems characterized by very short orbital periods, very low mass companions, and, in several cases, regular eclipses in their pulsed radio signal. Long-term timing revealed systematic but unpredictable variations in the orbital period, which can most likely be explained by the so-called Applegate mechanism. This relies on the magnetic dynamo activity generated inside the companion star and triggered by the pulsar wind, which induces a modification of the star's oblateness (or quadrupole variation). This, in turn, couples with the orbit by gravity, causing a consequent change in the orbital period. The Applegate description limits to provide estimates of physical quantities by highlighting their orders of magnitude. Therefore, we derive the time-evolution differential equations underlying the Applegate model, that is, we track such physical quantities in terms of time. Our strategy is to employ the orbital period modulations, measured by fitting the observational data, and implementing a highly accurate approximation scheme to finally reconstruct the dynamics of the spider system under study and the relative observables. Among the latter is the magnetic field activity inside the companion star, which is still a matter of debate for its complex theoretical modeling and the ensuing expensive numerical simulations. As an application, we exploit our methodology to examine two spider sources: 47 Tuc W (redback) and 47 Tuc O (black widow). The results obtained are analyzed and then discussed with the literature., Comment: 13 pages; 7 figures; 1 table; accepted for publication on Astronomy & Astrophysics

General Relativity suffers for two main problems which have not yet been overcome: it predicts spacetime singularities and cannot be formulated as a perturbative renormalizable theory. In particular, many attempts have been made for avoiding singularities, such as considering higher order or infinite derivative theories. The price to pay in both cases is to give up locality and therefore they are known altogether as non-local theories of gravity. In this paper, we investigate how to recognize the presence of non-local effects by exploiting the power emitted by gravitational waves in a binary system in presence of non-local corrections as $R\Box^{-1}R$ to the Hilbert-Einstein action. After solving the field equations in terms of the source stress-energy tensor $T_{\mu\nu}$ and obtaining the gravitational wave stress-energy pseudo-tensor, $\tau_{\mu\nu}$, we find that the General Relativity quadrupole formula is modified in a non-trivial way, making it feasible to find a possible signature of non-locality. Our final results on the gravitational wave stress-energy pseudo-tensor could also be applied to several astrophysical scenarios involving energy or momentum loss, potentially providing multiple tests for non-local deviations from General Relativity. We finally discuss the detectability of the massless transverse scalar mode, discovering that, although this radiation is extremely weak, in a small range around the model divergence, its amplitude could fall within the low-frequency Einstein Telescope sensitivity., Comment: 21 pages, 1 figure, accepted for publication in JCAP

The pulsar timing technique, which compares the observed arrival times of electromagnetic radiation from a pulsar with the predicted arrival times derived from a theoretical model of the pulsar system, is used in pulsar astronomy to infer a multitude of physical information and to constrain possible corrections to General Relativity (GR). The propagation delay is usually computed using formulas based on a post-Newtonian approach, for both the light trajectory and the orbital motion. However, evidence has recently emerged that this approximation may no longer be sufficient when the companion object is a supermassive black hole; deviations from a full GR computation of the propagation delay can reach a few seconds. In this paper, we analyze the case of binary pulsars with a stellar or intermediate black hole companion, whose discovery and timing are key goals of SKA. With a numerical algorithm, we have found that in this case, the full GR value depends only on the semi-major axis of the relative orbit and on the mass of the black hole companion. If the mass of the latter is sufficiently large ($100 M_{\odot}$), the maximum difference between the two approaches is significant ($\sim10^{-7}$ s) even for large binaries ($\sim10^{16}$ cm), and increases up to $\sim 10^{-4}$ s when the mass is $10^5 M_{\odot}$. We also consider relativistic corrections to the orbital motion, and discover that they can strongly affect the value of the propagation delay. We conclude that in the future, post-Newtonian formulas should be replaced with a more accurate approach in these systems, especially in view of future discoveries made by new large telescopes such as SKA.

We take up the investigation we left in the future-work stack in Giordano \textit{et al.} [``Fluid statics of a self-gravitational isothermal sphere of van der Waals' gas,'' Phys. Fluids \textbf{36}, 056127 (2024)], in which we pointed out the obvious necessity to inquire about the existence or absence of values of the characteristic numbers \itm{\alphay} and \itm{\betay} in correspondence to which the perfect-gas model's self gravitational effects, namely, upper boundedness of the gravitational number, spiraling behavior of peripheral density, oscillating behavior of central density, and the existence of multiple solutions corresponding to the same value of the gravitational number, appear also for the van der Waals' model. The development of our investigation brings to the conversion of our M$_{2}$ scheme based on a second-order differential equation into an equivalent system of two first-order differential equations that incorporates Milne's homology invariant variables. The converted scheme \fomt\ turns out to be much more efficacious than the M$_{2}$ scheme in terms of numerical calculations' easiness and richness of results. We use the perfect-gas model as benchmark to test the \fomt\ scheme; we re-derive familiar results and put them in a more general and rational perspective that paves the way to deal with the van der Waals' gas model. We introduce variable transformations that turn out to be the key to study (almost) analytically the monotonicity of the peripheral density with respect to variations of the gravitational number. The study brings to the proof that the gravitational number is not constrained by upper boundedness, the peripheral density does not spiral, and the central density does not oscillate for any couple of values assumed by the characteristic numbers $\alpha$ and $\beta$; however, multiple solutions ..., Comment: Revision according to published article (21 pages, 26 figures, 1 table)

Non-local theories of gravity are considered extended theories of gravity, meaning that when the non-local terms are canceled out, the limit of General Relativity (GR) is obtained. Several reasons have led us to consider this theory with increasing interest, but primarily non-locality emerges in a natural way as a side effect of the introduction of quantum corrections to GR, the purpose of which was to cure the singularity problem, both at astrophysical and cosmological level. In this paper we studied a peculiar case of the so called Deser-Woodard theory consisting in the addition of a non-local term to the Hilbert-Einstein lagrangian, and we derived for the first time contraints on the dimensionaless non-local parameter A by exploiting the predicted gravitational wave emission in three binary pulsars, namely PSR J1012+5307, PSR J0348+0432 and PSR $J1738+0333. We discovered that the instantaneous flux strongly depends on A and that the best constraints (0.12 < A < 0.16) come from PSR J1012+5307, for which the GR prediction is outside the observational ranges. However, since for PSR J1012 + 5307 scintillation is suspected, as emerged in a recent census by LOFAR, corruptions in pulsar timing could be hidden. We finally comment on the usability and reliability of this type of test for extended theories of gravity.

We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravitating isothermal sphere with the van der Waals' thermodynamic model, whose equation of state features well-known terms that account for molecular attraction and size. The governing equations are formulated for any thermodynamic model with two intensive degrees of freedom, applied with the van der Waals' model and solved numerically in nondimensional form by finite-difference algorithms. After a brief summary of thermodynamic characteristics possessed by the van der Waals' model, and relevant to the present study, we proceed to the description of the results in terms of comparative graphs illustrating radial profiles of density, pressure and gravitational field. We complement them with graphs that compare the dependence of central and wall densities on gravitational number for both perfect-gas and van der Waals' models and that attest dramatically and unequivocally how the presence of molecular-attraction and -size terms removes questionable fluid-statics results systematically found accompanying the perfect-gas model in standard treatments. We also describe, within a very brief and preliminary digression, how the sanitising action of the mentioned terms affects the thermodynamics of the isothermal sphere by providing evidence of how the gravitational correction to entropy corresponding to the van der Waals' model makes sure that there is no risk of gravothermal catastrophes, negative specific heats, and thermal instabilities. Furthermore, we investigate the phenomenology related to self-gravitationally induced both liquid-gas phase equilibria and metastable-gas states and we describe how they arise naturally and self-consistently from the governing equations. We conclude with a summary of the main results ..., Comment: Minor revision with correcte typos. 27 pages, 29 figures, 5 tables, 64 bibliographic references

Pulsars are rapidly rotating neutron stars emitting intense electromagnetic radiation that is detected on Earth as regular and precisely timed pulses. By exploiting their extreme regularity and comparing the real arrival times with a theoretical model (pulsar timing), it is possible to deduce many physical information, not only concerning the neutron star and its possible companion, but also the properties of the interstellar medium, up to tests of General Relativity. Last but not least, pulsars are used in conjunction with each other as a galactic-sized detector for the cosmic background of gravitational waves. In this paper, we investigate the effect of "matter" on the propagation time delay of photons emitted by a pulsar orbiting a spinning black hole, one of the most important relativistic effect in pulsar timing. We deduce an analytical formula for the time delay from geodesic equations, showing how it changes as the type of matter around the black hole (radiation, dust or dark energy) varies with respect to previous results, where matter has not been taken into account. It turns out that while the spin $a$ only induces a shift in the phase of the maximum delay without increasing or decreasing the delay, the effect of matter surrounding the black hole results in a noticeable alteration of it. Our results show that dark energy would give the strongest effect and that, interestingly, when the pulsar is positioned between the observer and the black hole a slightly lower pulse delay than in the no-matter case appears. We estimated these effects for SGR J1745-2900, the closest magnetar orbiting SgrA*.

We address two questions regarding square-well potentials from a didactic perspective. The first question concerns whether or not the justification of the standard a priori omission of the potential's vertical segments in the analysis of the eigenvalue problem is licit. The detour we follow to find out the answer considers a trapezoidal potential, includes the solution, analytical and numerical, of the corresponding eigenvalue problem and then analyzes the behavior of that solution in the limit when the slope of the trapezoidal potential's ramps becomes vertical. The second question, obviously linked to the first one, pertains whether or not eigenfunction's and its first derivative's continuity at the potential's jump points is justified as a priori assumption to kick-off the solution process, as it is standardly accepted in textbook approaches to the potential's eigenvalue problem., Comment: 45 pages, 14 figures, 3 tables

Non-linear electrodynamics (NLED) is a generalization of Maxwell's electrodynamics for strong fields. It could have significant implications for the study of black holes and cosmology and have been extensively studied in the literature, extending from quantum to cosmological contexts. Recently, its application to black holes, inflation and dark energy has caught on, being able to provide an accelerated Universe and address some current theoretical inconsistencies, such as the Big Bang singularity. In this work, we report two new ways to investigate these non-linear theories. First, we have analyzed the Blandford-Znajeck mechanism in light of this promising theoretical context, providing the general form of the extracted power up to second order in the black hole spin parameter $a$. We have found that, depending on the NLED model, the emitted power can be extremely increased or decreased, and that the magnetic field lines around the black hole seems to become vertical quickly. Considering only separated solutions, we have found that no monopole solutions exist and this could have interesting astrophysical consequences (not considered here). Last but not least, we attempted to confine the NLED parameters by inducing the amplification of primordial magnetic fields ('seeds'), thus admitting non-linear theories already during the early stages of the Universe. However, the latter approach proved to be useful for NLED research only in certain models. Our (analytical) results emphasize that the existence and behavior of non-linear electromagnetic phenomena strongly depend on the physical context and that only a power-low model seems to have any chance to compete with Maxwell., Comment: 18 pages

Segmenting medical images is critical to facilitating both patient diagnoses and quantitative research. A major limiting factor is the lack of labeled data, as obtaining expert annotations for each new set of imaging data and task can be labor intensive and inconsistent among annotators. We present CUTS, an unsupervised deep learning framework for medical image segmentation. CUTS operates in two stages. For each image, it produces an embedding map via intra-image contrastive learning and local patch reconstruction. Then, these embeddings are partitioned at dynamic granularity levels that correspond to the data topology. CUTS yields a series of coarse-to-fine-grained segmentations that highlight features at various granularities. We applied CUTS to retinal fundus images and two types of brain MRI images to delineate structures and patterns at different scales. When evaluated against predefined anatomical masks, CUTS improved the dice coefficient and Hausdorff distance by at least 10% compared to existing unsupervised methods. Finally, CUTS showed performance on par with Segment Anything Models (SAM, MedSAM, SAM-Med2D) pre-trained on gigantic labeled datasets., Comment: Accepted to the 27th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI 2024)

Black holes can accumulate a large amount of energy, responsible for highly energetic astrophysical phenomena Recently, fast magnetic reconnection (MR) of the magnetic field was proposed as a new way to extract energy and in this paper, we investigate this phenomena in a bumblebee Kerr-Sen BH. We find that the presence of the charge parameter strongly changes the simple Kerr case, making this extraction mechanism possible even for not extremely rotating black holes ($a \sim 0.7$). We also show that, under appropriate circumstances, MR is more efficient compared to the Blandford-Znajek mechanism. We finally compare these results with quintessence black-hole solutions not finding and enhancement respect to Kerr solution.

Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of the vector field along the Legendre orthonormal basis. Interestingly, this approach can be extended to cope with other orthonormal bases and, in particular, we here consider the case of the Chebyshev polynomial basis. The corresponding Runge-Kutta methods were previously obtained by Costabile and Napoli [33]. In this paper, the use of a different framework allows us to carry out a novel analysis of the methods also when they are used as spectral formulae in time, along with some generalizations of the methods., Comment: 25 pages, 2 figures, 2 tables

In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving corresponding fractional differential equations. A few numerical examples are reported., Comment: 8 pages, 3 figures

Do school openings trigger Covid-19 diffusion when school-age vaccination is available? We investigate this question using a unique geo-referenced high frequency database on school openings, vaccinations, and Covid-19 cases from the Italian region of Sicily. The analysis focuses on the change of Covid-19 diffusion after school opening in a homogeneous geographical territory. The identification of causal effects derives from a comparison of the change in cases before and after school opening in 2020/21, when vaccination was not available, and in 2021/22, when the vaccination campaign targeted individuals of age 12-19 and above 19. The results indicate that, while school opening determined an increase in the growth rate of Covid-19 cases in 2020/2021, this effect has been substantially reduced by school-age vaccination in 2021/2022. In particular, we find that an increase of approximately 10% in the vaccination rate of school-age population reduces the growth rate of Covid-19 cases after school opening by approximately 1.4%. In addition, a counterfactual simulation suggests that a permanent no vaccination scenario would have implied an increase of 19% in ICU beds occupancy.

In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Such methods admit an interesting interpretation in terms of continuous-stage Runge-Kutta methods, which is here recalled and revisited for general differential problems., Comment: 20 pages

In this paper we are concerned with numerical methods for the one-sided event location in discontinuous differential problems, whose event function is nonlinear (in particular, of polynomial type). The original problem is transformed into an equivalent Poisson problem, which is effectively solved by suitably adapting a recently devised class of energy-conserving methods for Poisson systems. The actual implementation of the methods is fully discussed, with a particular emphasis to the problem at hand. Some numerical tests are reported, to assess the theoretical findings., Comment: 14 pages, 1 figure, 2 tables

In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within the so-called line integral framework. Numerical tests to illustrate the theoretical findings are presented., Comment: 31 pages, 6 figures, 3 tables

In this paper we are concerned with energy-conserving methods for Poisson problems, which are effectively solved by defining a suitable generalization of HBVMs, a class of energy-conserving methods for Hamiltonian problems. The actual implementation of the methods is fully discussed, with a particular emphasis on the conservation of Casimirs. Some numerical tests are reported, in order to assess the theoretical findings., Comment: 30 pages, 5 figures, 3 tables

We describe the analytical solution of the eigenvalue problem introduced in our article mentioned in the title and relative to a punctiform electric charge confined in an one-dimensional box in the presence of an electric field. We also derive and discuss the analytical expressions of the external forces acting on the punctiform charge and associated with the boundaries of the one-dimensional box in the presence of the electric field., Comment: 9 pages, 2 figures, two tables; complement to D. Giordano and P. Amodio, European Journal of Physics, 42 065405 (33pp) (see also arxiv2011.04038 v3); accepted in European Journal of Physics (https://iopscience.iop.org/journal/0143-0807). This version contains changes requested by the referees and a few corrections of the text

We implement the PaperRank and AuthorRank indices introduced in [Amodio & Brugnano, 2014] in the Scopus database, in order to highlight quantitative and qualitative information that the bare number of citations and/or the h-index of an author are unable to provide. In addition to this, the new indices can be cheaply updated in Scopus, since this has a cost comparable to that of updating the number of citations. Some examples are reported to provide insight in their potentialities, as well as possible extensions., Comment: 20 pages, 3 figures, 4 tables. Accepted version on Journal of Infometrics

We describe a study motivated by our interest to examine the incompleteness of the Ehrenfest's theorem in quantum mechanics and to resolve a doubt regarding whether or not the hermiticity of the hamiltonian operator is sufficient to justify a simplification of the expression of the macroscopic-observable time derivative that promotes the one usually found in quantum-mechanics textbooks. The study develops by considering the simple quantum system "particle in one-dimensional box". We propose theoretical arguments to support the incompleteness of the Ehrenfest's theorem in the formulation he gave, in agreement with similar findings already published by a few authors, and corroborate them with the numerical example of an electric charge in an electrostatic field. The contents of this study should be useful to Bachelor and Master students; the style of the discussions is tailored to stimulate, we hope, the student's ability for independent thinking., Comment: 35 pages, 5 figures, 1 table. Fixed typo in Ref. [15]. Published in the European Journal of Physics (https://iopscience.iop.org/journal/0143-0807) on 16 September 2021 and updated on 14 October 2021

Unsupervised image-to-image translation consists of learning a pair of mappings between two domains without known pairwise correspondences between points. The current convention is to approach this task with cycle-consistent GANs: using a discriminator to encourage the generator to change the image to match the target domain, while training the generator to be inverted with another mapping. While ending up with paired inverse functions may be a good end result, enforcing this restriction at all times during training can be a hindrance to effective modeling. We propose an alternate approach that directly restricts the generator to performing a simple sparse transformation in a latent layer, motivated by recent work from cognitive neuroscience suggesting an architectural prior on representations corresponding to consciousness. Our biologically motivated approach leads to representations more amenable to transformation by disentangling high-level abstract concepts in the latent space. We demonstrate that image-to-image domain translation with many different domains can be learned more effectively with our architecturally constrained, simple transformation than with previous unconstrained architectures that rely on a cycle-consistency loss.

We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can handle both infinite and infinitesimal quantities symbolized by the positive and negative finite powers of the radix grossone. The computational features offered by the Infinity Computer allows us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort. An illustrative example about the solution of a nonlinear equation is also presented., Comment: 11 pages, 2 figures, 6 tables

In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known Lane-Emden equation, albeit under boundary conditions that differ from those usually assumed in the astrophysical literature. The existence of multiple solutions requires particular attention in devising appropriate numerical schemes apt to deal with and catch the solution multiplicity as efficiently and accurately as possible. In sequence, we describe some analytical properties of the model, the two algorithms used to obtain numerical solutions, and the numerical results for two selected cases., Comment: Revision accepted for publication in "Communications in Computational Physics"; 23 pages, 9 figures

In recent years, the class of energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) has been devised for numerically solving Hamiltonian problems. In this short note, we study their natural formulation as continuous-stage Runge-Kutta(-Nystr\"om) methods, which allows a deeper insight in the methods., Comment: 12 pages, accepted manuscript

We open the paper with introductory considerations describing the motivations of our long-term research plan targeting gravitomagnetism, illustrating the fluid-dynamics numerical test case selected for that purpose, that is, a perfect-gas sphere contained in a solid shell located in empty space sufficiently away from other masses, and defining the main objective of this study: the determination of the gravitofluid-static field required as initial field ($t=0$) in forthcoming fluid-dynamics calculations. The determination of the gravitofluid-static field requires the solution of the isothermal-sphere Lane-Emden equation. We do not follow the habitual approach of the literature based on the prescription of the central density as boundary condition; we impose the gravitational field at the solid-shell internal wall. As the discourse develops, we point out differences and similarities between the literature's and our approach. We show that the nondimensional formulation of the problem hinges on a unique physical characteristic number that we call gravitational number because it gauges the self-gravity effects on the gas' fluid statics. We illustrate and discuss numerical results; some peculiarities, such as gravitational-number upper bound and multiple solutions, lead us to investigate the thermodynamics of the physical system, particularly entropy and energy, and preliminarily explore whether or not thermodynamic-stability reasons could provide justification for either selection or exclusion of multiple solutions. We close the paper with a summary of the present study in which we draw conclusions and describe future work., Comment: 32 pages, 26 figures

Interest in image-to-image translation has grown substantially in recent years with the success of unsupervised models based on the cycle-consistency assumption. The achievements of these models have been limited to a particular subset of domains where this assumption yields good results, namely homogeneous domains that are characterized by style or texture differences. We tackle the challenging problem of image-to-image translation where the domains are defined by high-level shapes and contexts, as well as including significant clutter and heterogeneity. For this purpose, we introduce a novel GAN based on preserving intra-domain vector transformations in a latent space learned by a siamese network. The traditional GAN system introduced a discriminator network to guide the generator into generating images in the target domain. To this two-network system we add a third: a siamese network that guides the generator so that each original image shares semantics with its generated version. With this new three-network system, we no longer need to constrain the generators with the ubiquitous cycle-consistency restraint. As a result, the generators can learn mappings between more complex domains that differ from each other by large differences - not just style or texture.

Archetypal analysis is a data decomposition method that describes each observation in a dataset as a convex combination of "pure types" or archetypes. These archetypes represent extrema of a data space in which there is a trade-off between features, such as in biology where different combinations of traits provide optimal fitness for different environments. Existing methods for archetypal analysis work well when a linear relationship exists between the feature space and the archetypal space. However, such methods are not applicable to systems where the feature space is generated non-linearly from the combination of archetypes, such as in biological systems or image transformations. Here, we propose a reformulation of the problem such that the goal is to learn a non-linear transformation of the data into a latent archetypal space. To solve this problem, we introduce Archetypal Analysis network (AAnet), which is a deep neural network framework for learning and generating from a latent archetypal representation of data. We demonstrate state-of-the-art recovery of ground-truth archetypes in non-linear data domains, show AAnet can generate from data geometry rather than from data density, and use AAnet to identify biologically meaningful archetypes in single-cell gene expression data., Comment: 9 pages, 10 figures, to be presented at IEEE Big Data 2019

Unsupervised domain mapping has attracted substantial attention in recent years due to the success of models based on the cycle-consistency assumption. These models map between two domains by fooling a probabilistic discriminator, thereby matching the probability distributions of the real and generated data. Instead of this probabilistic approach, we cast the problem in terms of aligning the geometry of the manifolds of the two domains. We introduce the Manifold Geometry Matching Generative Adversarial Network (MGM GAN), which adds two novel mechanisms to facilitate GANs sampling from the geometry of the manifold rather than the density and then aligning two manifold geometries: (1) an importance sampling technique that reweights points based on their density on the manifold, making the discriminator only able to discern geometry and (2) a penalty adapted from traditional manifold alignment literature that explicitly enforces the geometry to be preserved. The MGM GAN leverages the manifolds arising from a pre-trained autoencoder to bridge the gap between formal manifold alignment literature and existing GAN work, and demonstrate the advantages of modeling the manifold geometry over its density.

Recently, the numerical solution of stiffly/highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in time. While a theoretical analysis of this spectral approach has been only partially addressed, there is enough numerical evidence that it turns out to be very effective even when applied to a wider range of problems. Here we fill this gap by providing a thorough convergence analysis of the methods and confirm the theoretical results with the aid of a few numerical tests., Comment: 18 pages, 1 figure

While neural networks are powerful approximators used to classify or embed data into lower dimensional spaces, they are often regarded as black boxes with uninterpretable features. Here we propose Graph Spectral Regularization for making hidden layers more interpretable without significantly impacting performance on the primary task. Taking inspiration from spatial organization and localization of neuron activations in biological networks, we use a graph Laplacian penalty to structure the activations within a layer. This penalty encourages activations to be smooth either on a predetermined graph or on a feature-space graph learned from the data via co-activations of a hidden layer of the neural network. We show numerous uses for this additional structure including cluster indication and visualization in biological and image data sets., Comment: 12 pages, 6 figures, presented at IDA 2020

While neural networks can be trained to map from one specific dataset to another, they usually do not learn a generalized transformation that can extrapolate accurately outside the space of training. For instance, a generative adversarial network (GAN) exclusively trained to transform images of black-haired men to blond-haired men might not have the same effect on images of black-haired women. This is because neural networks are good at generation within the manifold of the data that they are trained on. However, generating new samples outside of the manifold or extrapolating "out-of-sample" is a much harder problem that has been less well studied. To address this, we introduce a technique called neuron editing that learns how neurons encode an edit for a particular transformation in a latent space. We use an autoencoder to decompose the variation within the dataset into activations of different neurons and generate transformed data by defining an editing transformation on those neurons. By performing the transformation in a latent trained space, we encode fairly complex and non-linear transformations to the data with much simpler distribution shifts to the neuron's activations. We motivate our technique on an image domain and then move to our two main biological applications: removal of batch artifacts representing unwanted noise and modeling the effect of drug treatments to predict synergy between drugs.

It is increasingly common in many types of natural and physical systems (especially biological systems) to have different types of measurements performed on the same underlying system. In such settings, it is important to align the manifolds arising from each measurement in order to integrate such data and gain an improved picture of the system. We tackle this problem using generative adversarial networks (GANs). Recently, GANs have been utilized to try to find correspondences between sets of samples. However, these GANs are not explicitly designed for proper alignment of manifolds. We present a new GAN called the Manifold-Aligning GAN (MAGAN) that aligns two manifolds such that related points in each measurement space are aligned together. We demonstrate applications of MAGAN in single-cell biology in integrating two different measurement types together. In our demonstrated examples, cells from the same tissue are measured with both genomic (single-cell RNA-sequencing) and proteomic (mass cytometry) technologies. We show that the MAGAN successfully aligns them such that known correlations between measured markers are improved compared to other recently proposed models.

Recurrent neural networks have achieved remarkable success at generating sequences with complex structures, thanks to advances that include richer embeddings of input and cures for vanishing gradients. Trained only on sequences from a known grammar, though, they can still struggle to learn rules and constraints of the grammar. Neural Attribute Machines (NAMs) are equipped with a logical machine that represents the underlying grammar, which is used to teach the constraints to the neural machine by (i) augmenting the input sequence, and (ii) optimizing a custom loss function. Unlike traditional RNNs, NAMs are exposed to the grammar, as well as samples from the language of the grammar. During generation, NAMs make significantly fewer violations of the constraints of the underlying grammar than RNNs trained only on samples from the language of the grammar.