The current mainstream view in neuroscience and machine learning is that neural networks compress representations into low-dimensional manifolds [Op de Beeck et al., 2001, Gao and Ganguli, 2015, Gallego et al., 2017, Ansuini et al., 2019, Recanatesi et al., 2019]. A recent study challenges this view, by arguing that neural networks benefit form high-dimensional representations [Elmoznino and Bonner, 2022].

In contrast to these positions, we argue that learning in deep neural networks optimizes signal-to-noise processing. According to this view, neural networks may benefit form feature compression and expansion to (i) increase signal processing and (ii) diminish noise, while (iii) mapping inputs dimensions into outputs categories. We speculate also that nonlinearities (e.g., in activation functions) facilitate this process.

A causal relationship shall exist between the signal-to-noise ratio (SNR) and the behavioral performance of a network (e.g., in terms of classification accuracy) if SNRs are optimized through learning. To test this hypothesis, we introduced a SNR expression derived geometrically. Unlike the SNR expression in [Sorscher et al., 2022], our expression can be applied to neural representations associated with predictions of unseen data. We then computed the SNR to quantify the separability between category-based manifolds through different layers of neural processing, and tested the SNR with and without input noisy fluctuations, as well as with linear and nonlinear transformations (Linear, ReLU and Sigmoid).

Our results show that increasing noise fluctuations increases the dimensionality but diminishes the SNR and the accuracy, proving that higher dimensionality is not necessarily better in all conditions. In addition, we observe a causal correlation between SNR and accuracy in a perturbative analysis that gradually shortens the distance between the centroids of different category-based manifolds, without this analysis affecting the dimensionality of the data.

In addition, larger SNRs were obtained for nonlinear functions (ReLU and Sigmoid vs. Linear), which were correlated with higher accuracy ratios. Moreover, we found that the highest SNRs encountered were obtained for activations distributed within the region of maximum curvature of the sigmoid function, stressing the role of nonlinearities. We are currently exploring to what extent designed nonlinear functions with strong nonlinearities facilitate learning in neural networks with noisy data and robustness against adversarial examples.

Furthermore, we are testing if early-stopping, aimed to avoid overfitting during training, might be enhanced by considering the SNR.

References

H. Op de Beeck, J. Wagemans, and R. Vogels. Inferotemporal neurons represent low-dimensional configurations of parameterized shapes. Nat Neurosci, 4(12):1244-1252, Dec 2001.

P. Gao and S. Ganguli. On simplicity and complexity in the brave new world of large-scale neuroscience. Curr Opin Neurobiol, 32:148-155, Jun 2015.

J. A. Gallego, M. G. Perich, L. E. Miller, and S. A. Solla. Neural Manifolds for the Control of Movement. Neuron, 94(5):978-984, Jun 2017.

A. Ansuini, A. Laio, J. H. Macke, and D. Zoccolan. Intrinsic dimension of data representations in deep neural networks. Advances in Neural Information Processing Systems, 32, 2019.

S. Recanatesi, M. Farrell, M. Advani, T.Moore, G. Lajoie, and E. Shea-Brown. Dimensionality compression and expansion in deep neural networks. arXiv preprint arXiv:1906.00443, 2019.

E. Elmoznino and M. F. Bonner. High-performing neural networks models of visual cortex benefit from high latent dimensionality. bioRxiv, pages 2022-07, 2022.

B. Sorscher, S. Ganguli, and H. Sompolinsky. Neural representational geometry underlies few-shot concept learning . Proc Natl Acad Sci U S A, 119(43):e2200800119, Oct 2022.

The full Heusler alloys Mn₂MeZ, where Me is a 3d-metal and Z – an element of group III–V, attract the attention of researchers as materials promising for magnetoelectronic and thermoelectric applications [1]. These alloys may exhibit strong ferromagnetism or compensated ferrimagnetism up to high temperatures, phase transitions with a change in the magnetic structure are possible [2]. The magnetic measurements for the Mn₂YAl systems (Y = Cr, Mn, Fe) give zero total magnetization and may indicate compensated ferrimagnetism [2]. This work presents the results of calculations of the electronic structure and magnetic properties of two different phases of the Heusler alloy Mn₂CrAl. The first one is the cubic Fm-3m (space group 225) L2₁-type structure. The electronic structure of the Mn₂CrAl alloy was computed within GGA(+U) approaches. The latter method was used to take into account electron correlations in the Mn 3d shell for the value of Coulomb parameter ranging from 1 to 6 eV and the exchange (Hund) parameter equal to 0.86 eV. In our calculations, it was found that the electronic structure of Mn₂CrAl is metallic similar to Mn₂NiAl [3], and has a ferrimagnetic ordering of manganese atoms. The second phase of Mn₂CrAl is the cubic P4₁32 (space group 213) β-Mn-type one, which was also found to have a ferrimagnetic ordering with low values of moments of individual ions and the total moment equal to 0.12 µ_B/f.u. [4]. Thus, the calculated magnetic properties of the β-Mn-type phase of Mn₂CrAl are consistent with the experimental results [2], according to which the magnetization of this compound is close to zero.

The research was supported by the Russian Science Foundation, project no. 22-22-20109.

[1] C.Felser et al., APL Mater. 3, 041518 (2015).

[2] V.V.Marchenkov et al., JETP 155, 1083 (2019).

[3] E.D.Chernov et al., Magnetochemistry 9, 185 (2023).

[4] E.I.Shreder et al., Phys. Met. Metallogr. 124, 7 (2023).

With the populational rise in the last decades, the potable water available has been a common concern. In this scenario, pharmaceuticals, mostly excreted in sewers, are not treated by conventional wastewater treatment plants. This study explores the synthesis of a magnetic multi-core shell catalyst and its efficiency in the degradation of paracetamol (PCM) and sulfamethoxazole (SMX) by catalytic wet peroxide oxidation (CWPO). The catalysts were synthesized in a two-step process. The core was initially synthesized via a coprecipitation methodology, followed by the sol-gel synthesis of the niobium pentoxide shell. The tests were conducted with three different matrixes, two in single components ([SMX] =10 ppm or [PCM] =100 ppm) and one in multi-component ([SMX] = 10 ppm and [PCM] = 100 ppm). The liquid-phase oxidation reactions were carried out at 80 °C, pH 3.5, and stirring at 300 rpm and a catalysts concentration of 2.5 g L^-1. Results showed that the catalyst maintained its magnetic property, accelerating the removal process from the matrix and resisting the CWPO process, not showing leaching. The degradation of PCM and SMX in the single-component matrixes allowed removing about 90.9% of PCM and 22.8% of SMX in 4h. Still, the multi-component removed 88.7% of PCM and 80.1% of SMX in 4h, suggesting some synergy between the catalyst and the pharmaceuticals. In conclusion, the degradation of the pharmaceuticals by the new catalyst developed proved to have a high degradation rate and low toxicity.

Multinary chalcogenides Ⅰ₂-Ⅱ-Ⅳ-X₄ materials made from ecofriendly and abundant elements, namely Cu₂ZnSn(S,Se)₄ have received wide attention in the photovoltaic field. Recently, many researchers have focused on studying the behavior of their characteristic features through substituting of one or two of CZTS(e) constituents with isoelectronic elements in order to reduce the propensity of the system to form unwanted defects which hinder the improvement of photoelectric conversion capacity of this material. In this work, (Ag_xCu_1-x)₂ZnSnS₄ solid solution were synthetized via solid state method under vacuum. The impact of Ag substitution on the structural and optical properties of the as-prepared ACZTS samples has been systematically investigated. According to X-ray diffraction (XRD) analysis, a noticeable change in the structural features of (Ag_xCu_1-x)₂ZnSnS₄ samples has been observed. The diffraction lines are slightly shifted to lower angles with increasing Ag content, and the dominant tetragonal phase with a kesterite (CZTS) type-structure is gradually shifted into tetragonal perquitasite-type AZTS structure as a result of the appearance of peaks associated with the letter structure. The lattice constants of (Ag_xCu_1-x)₂ZnSnS₄ deviate from Vegard's law as a consequence of defects formation during the synthesis. UV-Vis diffuse reflectance measurements showed that optical properties could be tuned by varying the Ag content, however, due to the presence of secondary phases, the variation of the band gap does not depend linearly on Ag concentrations.

Our study provides a useful path for better understanding the effect of Ag-substitution on the structural and optical properties of CZTS.

This article proposes the Differential Entropy-based Compactness Index (DECI), a novel metric for synthetically describing the spatial distribution of point clouds. The index is based on the calculation of the differential entropy of each point in the point clouds. If the point clouds represent a spatial distribution of moving objects, making them time-dependent, one of the key advantages of DECI is its capability for real-time monitoring. Moreover, analyzing historical data enables the study of DECI trends, point dynamics, and average values within specific intervals. It also allows for the comparison of two or more point clouds. While DECI primarily characterizes the spatial distribution of points, the paper proposes several practical applications. Notably, DECI can serve as a measure of risk and congestion, making it relevant in various engineering domains, particularly in controlling maritime, aerial, and road traffic (including autonomous driving) and identifying areas in need of infrastructure improvements. It is also applicable for assessing crowd density and risks in public, outdoor, and indoor spaces. The versatility of DECI extends to the health and biological fields, and it holds significance in team sports analysis, where it can examine the influence of compactness on match results. The ability of DECI to capture real-time dynamics and historical models makes it invaluable for decision-making and optimizing various aspects of system management. Additionally, this index could be considered a valuable feature for Machine Learning applications.

Research on distributed optical fiber sensing techniques is advancing rapidly, particularly in the field of strain and temperature sensing using Brillouin scattering. Among the proposed Brillouin sensors, Brillouin optical correlation-domain reflectometry (BOCDR) utilizes spontaneous Brillouin scattering. BOCDR operates by injecting light into one end of a measurement fiber (FUT) and boasts unique features such as millimeter-scale spatial resolution, random access capability, and cost-effectiveness. It employs a method that synthesizes the optical coherence functions, enabling interference between modulated signal light and reference light, resulting in "correlation peaks" along the FUT. By scanning these peaks, the distribution of the Brillouin gain spectrum can be obtained, maintaining a constant ratio between spatial resolution and measurement range. In conventional systems, only one correlation peak is present within the FUT, limiting the measurement range. However, approaches including time gating, dual modulation, and chirp modulation have been proposed to extend the range while preserving spatial resolution, albeit at higher device and design costs. To overcome this limitation, our study introduces the "differential spectrum method" for measuring strain distribution near the open end of the FUT, beyond the theoretical measurement range. Assuming a constant temperature and the absence of strain application sections along the proximal part of the FUT, this method generates multiple correlation peaks within the FUT and utilizes signal processing techniques to eliminate scattering effects from correlation peaks other than the measurement point. This cost-effective and straightforward approach enables strain distribution measurement in remote locations.

Strain and temperature sensors based on Brillouin scattering in optical fibers have garnered interest for their ability to measure strain and temperature distributions, making them highly applicable to structural health monitoring. Here we focus on a method that observes the spectrum of spontaneous Brillouin scattering throughout the entire length of the fiber under test (FUT) by injecting light into one end of the FUT. Generally, the precise observation of the Brillouin gain spectrum (BGS) using the frequency resolution of an optical spectrum analyzer is challenging, thus requiring the use of self-heterodyne detection. This method involves interfering the scattered light from the FUT with the reference light and converting the beat frequency component into an electrical signal, which is then observed using an electrical spectrum analyzer. Recently, efforts have been made to simplify the Brillouin observation system and reduce costs. One approach involves eliminating the independent reference light path. Previously proposed methods utilized the Fresnel-reflected light at the air boundary of the FUT open end and the boundary between the second port of an optical circulator and the FUT as reference light sources. However, controlling the power of the Fresnel-reflected light, which remained constant in these methods, made it difficult to maximize the signal-to-noise ratio (SNR) of the BGS. Therefore, in this study, we attempted to maximize the SNR of the observed BGS by eliminating the reference light path and instead controlling the reflectivity using a tunable reflectivity mirror placed at the open end of the FUT.

Deep learning models are applied in precision agriculture for site-specific weed management. This is done by classifying and detecting weeds in farmlands. However, due to their largeness in size, they are rarely adopted in resource-constrained devices (like edge devices) used in precision agriculture. In this study, we propose a lightweight deep learning model for detecting weeds in corn and soybean plants. We used transfer learning to train a MobilenetV2 model for detecting weeds in corn and soybean. The dataset used consists of 5773 samples of corn, soybean, and weeds. The model reached a classification accuracy of 96% but the size of it. We then applied the quantization technique to reduce the size of the model, and also increase latency so it can be deployed on edge devices. The MobilenetV2 model achieved an accuracy of 96% while the quantized model has an accuracy of 90%. Also, the quantized model is three times lesser in size than the original MobilenetV2 model. The results show that quantization can be used to reduce the size of a model, yet maintain a reasonable amount of its accuracy.

This paper represents a three-species food web model based on the interactions between
susceptible prey, infected prey, and predator species. It is considered that in the absence of
predator species and prey species grow logistically. Predators consume susceptible and infected
prey in the form of Crowley-Martin and Beddington-DeAngelis Functional Responses. Also,
infected prey consumes susceptible prey in the form of Holling type II interactions.
Positiveness, boundedness and positive invariance are examined. All biologically feasible
equilibrium points are investigated. The local stability of these equilibrium points and their
global stability are analysed by suitable Lyapunov functions of these equilibrium points.
Finally, numerical solutions are analyzed according to our findings.

Plateau surfaces have excellent sliding properties, because only the high peaks of surface asperity are smoothed. Therefore, they form the sliding surfaces of automobile engines and machine tools, contributing to their high performance and low environmental impact. As the development and production of these machines require the evaluation of their plateau surface components, methods for plateau surface evaluation have been proposed by the International Organization for Standardization (ISO) and previous researches. These evaluation methods include a processing procedure for fitting a hyperbola to the material probability curve (MPC) of the plateau surface. However, the ISO standard does not clearly state the rationale for restricting the fitting curve to a hyperbola. As shown in a previous study, another curve that can fit the shape of the MPC of the plateau surface is expected to be a parabola in addition to a hyperbola. The parabola and hyperbola are curves known as conic sections
. In this research, we examine the validity of hyperbolic curve fitting and explore the fitting of conic curve by utilizing the information of conjugate diameters. Approximations using a curve better suited to the shape of the MPCs of the plateau surface can anticipate to the realization of higher quality evaluations of the surface. Through this research, we aim to contribute to the development of industry as well as improve the performance and environmental impact of automobile engines and machine tools.