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Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robustness. These fluctuations can be categorized as intrinsic, stemming from the system's inherent structure and dynamics, and extrinsic, arising from external factors, such as temperature variations. Understanding the interplay between these fluctuations is crucial for obtaining a comprehensive understanding of biological phenomena. However, studying these effects poses significant computational challenges. In this study, we used an underexplored methodology to analyze the effect of extrinsic fluctuations in stochastic systems using ordinary differential equations instead of solving the Master Equation with stochastic parameters. By incorporating temperature fluctuations into reaction rates, we explored the impact of extrinsic factors on system dynamics. We constructed a master equation and calculated the equations for the dynamics of the first two moments, offering computational efficiency compared with directly solving the chemical master equation. We applied this approach to analyze a biological oscillator, focusing on the p53 model and its response to temperature-induced extrinsic fluctuations. Our findings underscore the impact of extrinsic fluctuations on the nature of oscillations in biological systems, with alterations in oscillatory behavior depending on the characteristics of extrinsic fluctuations. We observed an increased oscillation amplitude and frequency of the p53 concentration cycle. This study provides valuable insights into the effects of extrinsic fluctuations on biological oscillations and highlights the importance of considering them in more complex systems to prevent unwanted scenarios related to health issues., Comment: 21 pages, 9 figures

In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination of analytical expressions for the mean and variance in an exact form and thus valid for any system size. In particular, this approach was used to study Bernoulli-Laplace and Ehrenfest urns, for which analytic expressions describing their evolution were found. This approach and the results will contribute to a more comprehensive understanding of stochastic systems and statistical physics for small-sized systems, where the thermodynamic limit cannot be assumed., Comment: 6 pages, 5 figures

In this paper we study the space $\mathbb{L}(n)$ of $n$-gons in the plane degenerated to segments. We prove that this space is a smooth real submanifold of $\mathbb{C}^n$, and describe its topology in terms of the manifold $\mathbb{M}(n)$ of $n$-gons degenerated to segments and with the first vertex at 0. We show that $\mathbb{M}(n)$ and $\mathbb{L}(n)$ contain straight lines that form a basis of directions in each one of their tangent spaces, and we compute the geodesic equations in these manifolds. Finally, the quotient of $\mathbb{L}(n)$ by the diagonal action of the affine complex group and the re-enumeration of the vertices is described., Comment: 17 pages, 1 figure

Catheter ablation (CA) remains the cornerstone alternative to cardioversion for sinus rhythm (SR) restoration in patients with atrial fibrillation (AF). Unfortunately, despite the last methodological and technological advances, this procedure is not consistently effective in treating persistent AF.

The article introduces the stochastic N-k interdiction problem for power grid operations and planning that aims to identify a subset of k components (out of N components) that maximizes the expected damage, measured in terms of load shed. Uncertainty is modeled through a fixed set of outage scenarios, where each scenario represents a subset of components removed from the grid. We formulate the stochastic N-k interdiction problem as a bi-level optimization problem and propose two algorithmic solutions. The first approach reformulates the bi-level stochastic optimization problem to a single level, mixed-integer linear program (MILP) by dualizing the inner problem and solving the resulting problem directly using a MILP solver to global optimality. The second is a heuristic cutting-plane approach, which is exact under certain assumptions. We compare these approaches in terms of computation time and solution quality using the IEEE-Reliability Test System and present avenues for future research., Comment: 6 pages, 2 figures

"Objective: The electrocardiogram (ECG) is currently the most widely used recording to diagnose cardiac disorders, including the most common supraventricular arrhythmia, such as atrial fibrillation (AF). However, different types of electrical disturbances, in which power-line interference (PLI) is a major problem, can mask and distort the original ECG morphology. This is a significant issue in the context of AF, because accurate characterization of fibrillatory waves (f-waves) is unavoidably required to improve current knowledge about its mechanisms. This work introduces a new algorithm able to reduce high levels of PLI and preserve, simultaneously, the original ECG morphology. Approach: The method is based on stationary wavelet transform shrinking and makes use of a new thresholding function designed to work successfully in a wide variety of scenarios. In fact, it has been validated in a general context with 48 ECG recordings obtained from pathological and non-pathological conditions, as well as in the particular context of AF, where 380 synthesized and 20 long-term real ECG recordings were analyzed. Main results: In both situations, the algorithm has reported a notably better performance than common methods designed for the same purpose. Moreover, its effectiveness has proven to be optimal for dealing with ECG recordings affected by AF, since f-waves remained almost intact after removing very high levels of noise. Significance: The proposed algorithm may facilitate a reliable characterization of the f-waves, preventing them from not being masked by the PLI nor distorted by an unsuitable filtering applied to ECG recordings with AF."

Surgical ablation (SA) is the most effective procedure to terminate atrial fibrillation (AF) in patients requiring concomitant open heart surgery. However, considering the great stress provoked in the patients heart, along with the benefits of anticipating antiarrhythmic therapeutical decisions, preoperative prediction of long term failure of the procedure is an interesting clinical challenge. Hence, the present work introduces a novel algorithm to anticipate SA outcome after one year of follow up by just analyzing the surface ECG. The method firstly extracts fibrillatory waves reflected on standard lead V1 using an adaptive QRST cancellation approach. The resulting signal is then segmented into 1 s length intervals and wavelet energy is computed for all of them. Finally, the coefficient of variation of the time series obtained for the 7th scale is computed. Analyzing 20 second length preoperative ECG excerpts from 53 persistent AF patients undergoing concomitant openheart surgery, only the proposed method reported statistically significant differences between the patients who relapsed to AF and those who maintained sinus rhythm during the follow up. The algorithm also provided values of sensitivity, specificity, and accuracy between 10 and 20% better than the well established dominant atrial frequency and fibrillatory waves amplitude, thus suggesting to be a promising predictor of AF recurrence after SA.

Nowadays, the electrocardiogram (ECG) is still the most widely used signal for the diagnosis of cardiac pathologies. However, this recording is often disturbed by the powerline interference (PLI), its removal being mandatory to avoid misdiagnosis. Although a broad variety of methods have been proposed for that purpose, often they substantially alter the original signal morphology or are computationally expensive. Hence, the present work introduces a simple and efficient algorithm to suppress the PLI from the ECG. Briefly, the input signal is decomposed into four Wavelet levels and the resulting coefficients are thresholded to remove the PLI estimated from the TQ intervals. The denoised ECG signal is then reconstructed by computing the inverse Wavelet transform. The method has been validated making use of fifty 10-min length clean ECG segments obtained from the MIT BIH Normal Sinus Rhythm database, which were contaminated with a sinusoidal signal of 50 Hz and variable harmonic content. Comparing the original and denoised ECG signals through a signed correlation index, improvements between 10 - 72% have been observed with respect to common adaptive notch filtering, implemented for comparison. These results suggest that the proposed method is featured by an enhanced trade-off between noise reduction and signal morphology preservation.

The Hill function is relevant for describing enzyme binding and other processes in gene regulatory networks. Despite its theoretical foundation, it is often empirically used as a useful fitting function. Theoretical predictions suggest that the Hill coefficient should be an integer. However, it is often assigned a decimal value. The deterministic approximation of binding processes leads to the derivation of the Hill function, which can be expanded around the fluctuation magnitude to derive mesoscopic corrections. This study establishes the relationships between intermediate processes and the decimal Hill coefficient through a direct relationship between the dissociation constants, both with and without fluctuations. This outcome contributes to a deeper understanding of the underlying processes associated with the decimal Hill coefficient while also enabling the prediction of an effective value of the Hill coefficient from the underlying mechanism. This procedure allows us to have a simplified effective description of complex systems., Comment: 12 pages, 9 figures

Quantum Key Distribution (QKD) promises a provably secure method to transmit information from one party to another. Free-space QKD allows for this information to be sent over great distances and in places where fibre-based communications cannot be implemented, such as ground-satellite. The primary limiting factor for free-space links is the effect of atmospheric turbulence, which can result in significant error rates and increased losses in QKD channels. Here, we employ the use of a high-speed Adaptive Optics (AO) system to make real-time corrections to the wavefront distortions on spatial modes that are used for high-dimensional QKD in our turbulent channel. First, we demonstrate the effectiveness of the AO system in improving the coupling efficiency of a Gaussian mode that has propagated through turbulence. Through process tomography, we show that our system is capable of significantly reducing the crosstalk of spatial modes in the channel. Finally, we show that employing AO reduces the quantum dit error rate for a high-dimensional orbital angular momentum-based QKD protocol, allowing for secure communication in a channel where it would otherwise be impossible. These results are promising for establishing long-distance free-space QKD systems., Comment: 8 pages, 5 figures, supplemetary material included

We provide two new exact Sidon-Ramsey numbers to the list known so far. We also improve the upper bounds of the next two Sidon-Ramsey numbers. In doing so, we comment on the tendencies we found on the Sidon-Ramsey partitions that were studied to obtain these results.

Describing reaction rates in stochastic bio-circuits is commonly done by directly introducing the deterministically deduced Hill function into the master equation. However, when fluctuations in enzymatic reaction rates are not neglectable, the Hill function must be derived, considering all the involved stochastic reactions. In this work, we derived the stochastic version of the Hill function from the master equation of the complete set of reactions that, in the macroscopic limit, lead to the Hill function reaction rate. We performed a series expansion around the average values of the concentrations, which allowed us to find corrections for the deterministic Hill function. This process allowed us to quantify the fluctuations of enzymatic reactions. We found that the underlying variability in propensity rates of gene regulatory networks has an important non-linear effect that reduces the intrinsic fluctuations of the mRNA and protein concentrations., Comment: 23 pages, 14 figures

Low-dimensional topological objects, such as knots and braids, have become prevalent in multiple areas of physics, such as fluid dynamics, optics, and quantum information processing. Such objects also now play a role in cryptography, where a framed knot can store encoded information using its braid representation for communications purposes. The greater resilience of low-dimensional topological elements under deformations allows them to be employed as a reliable framework for information exchange. Here, we introduce a challenge-response protocol as an application of this construction for authentication. We provide illustrative examples of both procedures showing how framed links and braids may help to enhance secure communication., Comment: 5 pages, 4 figures

Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various physical phenomena, notably the emergence of topological invariants of many-body states. Recently it has been demonstrated that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. Furthermore, it has been predicted that such geometric phases may exhibit a topological transition as function of the measurement strength. Here, we demonstrate and study this transition experimentally employing an optical platform. We show the robustness to certain generalizations of the original protocol, as well as to certain types of imperfections. Our protocol can be interpreted in terms of environment-induced geometric phases.

This paper describes and validates for the first time the dynamic modelling of Liquid Crystal (LC)-based planar multi-resonant cells, as well as its use as bias signals synthesis tool to improve their reconfigurability time. The dynamic LC director equation is solved in the longitudinal direction through the finite elements method, which provides the z- and time-dependent inhomogeneous permittivity tensor used in an electromagnetic simulator to evaluate the cells behaviour. The proposed model has been experimentally validated using reflective cells for phase control (reflectarray) and measuring the transient phase, both in excitation and relaxation regimes. It is shown how a very reduced number of stratified layers are needed to model the material inhomogeneity, and that even an homogeneous effective tensor can be used in most of the cases, which allows a model simplification suitable for design procedures without losing accuracy. Consequently, a novel bias signal design tool is proposed to significantly reduce the transition times of LC cells, and hence, of electrically large antennas composed of them. These tools, similar to those used in optical displays, are experimentally validated for the first time at mm- and sub-mm wave frequencies in this work, obtaining an improvement of orders of magnitude., Comment: This paper has been accepted at IEEE Transactions on Antennas and Propagation

Based on the data gathered by echo-sounder buoys attached to drifting Fish Aggregating Devices (dFADs) across tropical oceans, the current study applies a Machine Learning protocol to examine the temporal trends of tuna schools' association to drifting objects. Using a binary output, metrics typically used in the literature were adapted to account for the fact that the entire tuna aggregation under the dFAD was considered. The median time it took tuna to colonize the dFADs for the first time varied between 25 and 43 days, depending on the ocean, and the longest soak and colonization times were registered in the Pacific Ocean. The tuna schools' Continuous Residence Times were generally shorter than Continuous Absence Times (median values between 5 and 7 days, and 9 and 11 days, respectively), in line with the results found by previous studies. Using a regression output, two novel metrics, namely aggregation time and disaggregation time, were estimated to obtain further insight into the symmetry of the aggregation process. Across all oceans, the time it took for the tuna aggregation to depart from the dFADs was not significantly longer than the time it took for the aggregation to form. The value of these results in the context of the "ecological trap" hypothesis is discussed, and further analyses to enrich and make use of this data source are proposed.

Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze quantum random walks implemented by coherent light propagation in series-coupled photonic ring resonators. We propose a family of graphs modeling these devices and compare quantum and classical random walks on these structures, calculating steady-state and time-dependent solutions. We obtain conditions for quantum advantage in this setting and show how to recover classical random walks by averaging over quantum phases. Preliminary device feasibility tests are carried out via simulations and experimental results using polymeric directional couplers., Comment: 11 pages + 9-page appendix, 13 figures

For a given positive integer $k$, the Sidon-Ramsey number $\SR(k)$ is defined as the minimum value of $n$ such that, in every partition of the set $[1, n]$ into $k$ parts, there exists a part that contains two distinct pairs of numbers with the same sum. In other words, there is a part that is not a Sidon set. In this paper, we investigate the asymptotic behavior of this parameter and two generalizations of it. The first generalization involves replacing pairs of numbers with $h$-tuples, such that in every partition of $[1, n]$ into $k$ parts, there exists a part that contains two distinct $h$-tuples with the same sum. Alternatively, there is a part that is not a $B_h$ set. The second generalization considers the scenario where the interval $[1, n]$ is substituted with a non-necessarily symmetric $d$-dimensional box of the form $\prod_{i=1}^d[1,n_i]$. For the general case of $h\geq 3$ and non-symmetric boxes, before applying our method to obtain the Ramsey-type result, we needed to establish an upper bound for the corresponding density parameter., Comment: 11 pages

Echo-sounder data registered by buoys attached to drifting FADs provide a very valuable source of information on populations of tuna and their behaviour. This value increases whenthese data are supplemented with oceanographic data coming from CMEMS. We use these sources to develop Tuna-AI, a Machine Learning model aimed at predicting tuna biomass under a given buoy, which uses a 3-day window of echo-sounder data to capture the daily spatio-temporal patterns characteristic of tuna schools. As the supervised signal for training, we employ more than 5000 set events with their corresponding tuna catch reported by the AGAC tuna purse seine fleet.