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We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for $pp \rightarrow t\bar{t}j$. We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical '${\rm d} \log$' form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically on $\epsilon$ and contains non-logarithmic one-forms in addition to the canonical ${\rm d} \log$'s. We solve the systems of differential equations numerically using generalised series expansions with the boundary terms obtained using the auxiliary mass flow method. A summary of all one-loop and two-loop planar topologies is presented including the list of alphabet letters for the '${\rm d} \log$' form systems and high-precision boundary values., Comment: 22 pages, 7 figures, 3 tables, 3 appendices

We study the minority-opinion dynamics over a fully-connected network of $n$ nodes with binary opinions. Upon activation, a node receives a sample of opinions from a limited number of neighbors chosen uniformly at random. Each activated node then adopts the opinion that is least common within the received sample. Unlike all other known consensus dynamics, we prove that this elementary protocol behaves in dramatically different ways, depending on whether activations occur sequentially or in parallel. Specifically, we show that its expected consensus time is exponential in $n$ under asynchronous models, such as asynchronous GOSSIP. On the other hand, despite its chaotic nature, we show that it converges within $O(\log^2 n)$ rounds with high probability under synchronous models, such as synchronous GOSSIP. Finally, our results shed light on the bit-dissemination problem, that was previously introduced to model the spread of information in biological scenarios. Specifically, our analysis implies that the minority-opinion dynamics is the first stateless solution to this problem, in the parallel passive-communication setting, achieving convergence within a polylogarithmic number of rounds. This, together with a known lower bound for sequential stateless dynamics, implies a parallel-vs-sequential gap for this problem that is nearly quadratic in the number $n$ of nodes. This is in contrast to all known results for problems in this area, which exhibit a linear gap between the parallel and the sequential setting., Comment: 27 pages, 1 figure, to be published in SODA 2024

We report on recent progress for the QCD corrections to top quark pair plus jet production. In particular, we discuss a recent computation for the two-loop master integrals associated to a two-loop five-point pentagon-box integral configuration with one internal massive propagator, that contributes to top quark pair production in association with a jet in the QCD planar limit., Comment: Proceedings for Radcor 2023, 8 pages, 1 figure

We present the computation of the two-loop form factors for diphoton production in the quark annihilation channel. These quantities are relevant for the NNLO QCD corrections to diphoton production at LHC recently presented in arXiv:2308.10885. The computation is performed retaining full dependence on the mass of the heavy quark in the loops. The master integrals are evaluated by means of differential equations which are solved exploiting the generalised power series technique., Comment: 23 pages, 5 figures

In this paper we consider the diphoton production in hadronic collisions at the next-to-next-to-leading order (NNLO) in perturbative QCD, taking into account for the first time the full top quark mass dependence up to two loops (full NNLO). We show selected numerical distributions, highlighting the kinematic regions where the massive corrections are more significant. We make use of the recently computed two-loop massive amplitudes for diphoton production in the quark annihilation channel. The remaining massive contributions at NNLO are also considered, and we comment on the weight of the different types of contributions to the full and complete result., Comment: 14 pages and 5 figures

Opinion diffusion is a crucial phenomenon in social networks, often underlying the way in which a collective of agents develops a consensus on relevant decisions. The voter model is a well-known theoretical model to study opinion spreading in social networks and structured populations. Its simplest version assumes that an updating agent will adopt the opinion of a neighboring agent chosen at random. The model allows us to study, for example, the probability that a certain opinion will fixate into a consensus opinion, as well as the expected time it takes for a consensus opinion to emerge. Standard voter models are oblivious to the opinions held by the agents involved in the opinion adoption process. We propose and study a context-dependent opinion spreading process on an arbitrary social graph, in which the probability that an agent abandons opinion $a$ in favor of opinion $b$ depends on both $a$ and $b$. We discuss the relations of the model with existing voter models and then derive theoretical results for both the fixation probability and the expected consensus time for two opinions, for both the synchronous and the asynchronous update models.

We investigate opinion dynamics in a fully-connected system, consisting of $n$ identical and anonymous agents, where one of the opinions (which is called correct) represents a piece of information to disseminate. In more detail, one source agent initially holds the correct opinion and remains with this opinion throughout the execution. The goal for non-source agents is to quickly agree on this correct opinion, and do that robustly, i.e., from any initial configuration. The system evolves in rounds. In each round, one agent chosen uniformly at random is activated: unless it is the source, the agent pulls the opinions of $\ell$ random agents and then updates its opinion according to some rule. We consider a restricted setting, in which agents have no memory and they only revise their opinions on the basis of those of the agents they currently sample. As restricted as it is, this setting encompasses very popular opinion dynamics, such as the voter model and best-of-$k$ majority rules. Qualitatively speaking, we show that lack of memory prevents efficient convergence. Specifically, we prove that no dynamics can achieve correct convergence in an expected number of steps that is sub-quadratic in $n$, even under a strong version of the model in which activated agents have complete access to the current configuration of the entire system, i.e., the case $\ell=n$. Conversely, we prove that the simple voter model (in which $\ell=1$) correctly solves the problem, while almost matching the aforementioned lower bound. These results suggest that, in contrast to symmetric consensus problems (that do not involve a notion of correct opinion), fast convergence on the correct opinion using stochastic opinion dynamics may indeed require the use of memory. This insight may reflect on natural information dissemination processes that rely on a few knowledgeable individuals.

Motivation: Over the past decade, network-based approaches have proven useful in identifying disease modules within the human interactome, often providing insights into key mechanisms and guiding the quest for therapeutic targets. This is all the more important, since experimental investigation of potential gene candidates is an expensive task, thus not always a feasible option. On the other hand, many sources of biological information exist beyond the interactome and an important research direction is the design of effective techniques for their integration. Results: In this work, we introduce the Biological Random Walks (BRW) approach for disease gene prioritization in the human interactome. The proposed framework leverages multiple biological sources within an integrated framework. We perform an extensive, comparative study of BRW's performance against well-established baselines. Availability and implementation: All code is publicly available and can be downloaded at \url{https://github.com/LeoM93/BiologicalRandomWalks}. We used publicly available datasets, details on their retrieval and preprocessing are provided in the supplementary material.

We present the analytic expressions for the two-loop form factors for the production or decay of pseudo-scalar quarkonia, in a scheme where the quarks are produced at threshold. We consider the two-loop amplitude for the process $\gamma \gamma \leftrightarrow {^1S_0^{[1]}}$, that was previously known only numerically, as well as for the processes $gg \leftrightarrow {^1S_0^{[1]}}$, $\gamma g \leftrightarrow {^1S_0^{[8]}}$ and $gg \leftrightarrow {^1S_0^{[8]}}$, which have not been computed before. The two-loop corrections to $gg \leftrightarrow {^1S_0^{[1]}}$ are the last missing ingredients for a full NNLO calculation of $\eta_Q$ hadro-production. We discuss how the singularity structure of the amplitudes is affected by the threshold kinematics, which in particular introduces Coulomb singularities. In this context, we first show how the usual structure of the infrared singularities degenerates at threshold kinematics, and then extract the anomalous dimensions governing the Coulomb singularities for colour-singlet and octet channels, the latter being presented here for the first time. We give high-precision numerical results for the hard functions, which can be used for phenomenological studies of $\eta_Q$ production and decay at NNLO., Comment: 37 pages, 1 figure, v2: version published in JHEP

We consider the case of a two-loop five-point pentagon-box integral configuration with one internal massive propagator that contributes to top-quark pair production in association with a jet at hadron colliders. We construct the system of differential equations for all the master integrals in a canonical form where the analytic form is reconstructed from numerical evaluations over finite fields. We find that the system can be represented as a sum of d-logarithmic forms using an alphabet of 71 letters. Using high precision boundary values obtained via the auxiliary mass flow method, a numerical solution to the master integrals is provided using generalised power series expansions., Comment: 31 pages, 47 figures, ancillary material attached to the submission. Version v3 as published in JHEP

Motivation: Genome-wide association studies (GWAS) have successfully identified thousands of genetic risk loci for complex traits and diseases. Most of these GWAS loci lie in regulatory regions of the genome and the gene through which each GWAS risk locus exerts its effects is not always clear. Many computational methods utilizing biological data sources have been proposed to identify putative casual genes at GWAS loci; however, these methods can be improved upon. Results: We present the Relations-Maximization Method, a dense module searching method to identify putative causal genes at GWAS loci through the generation of candidate sub-networks derived by integrating association signals from GWAS data into the gene co-regulation network. We employ our method in a chronic obstructive pulmonary disease GWAS. We perform an extensive, comparative study of Relations-Maximization Method's performance against well-established baselines.

In the Random Subset Sum Problem, given $n$ i.i.d. random variables $X_1, ..., X_n$, we wish to approximate any point $z \in [-1,1]$ as the sum of a suitable subset $X_{i_1(z)}, ..., X_{i_s(z)}$ of them, up to error $\varepsilon$. Despite its simple statement, this problem is of fundamental interest to both theoretical computer science and statistical mechanics. More recently, it gained renewed attention for its implications in the theory of Artificial Neural Networks. An obvious multidimensional generalisation of the problem is to consider $n$ i.i.d. $d$-dimensional random vectors, with the objective of approximating every point $\mathbf{z} \in [-1,1]^d$. In 1998, G. S. Lueker showed that, in the one-dimensional setting, $n=\mathcal{O}(\log \frac 1\varepsilon)$ samples guarantee the approximation property with high probability.In this work, we prove that, in $d$ dimensions, $n = \mathcal{O}(d^3\log \frac 1\varepsilon \cdot (\log \frac 1\varepsilon + \log d))$ samples suffice for the approximation property to hold with high probability. As an application highlighting the potential interest of this result, we prove that a recently proposed neural network model exhibits universality: with high probability, the model can approximate any neural network within a polynomial overhead in the number of parameters.

We compute the master integrals relevant for the two-loop corrections to pseudo-scalar quarkonium and leptonium production and decay. We present both analytic and high-precision numerical results. The analytic expressions are given in terms of multiple polylogarithms (MPLs), elliptic multiple polylogarithms (eMPLs) and iterated integrals of Eisenstein series. As an application of our results, we obtain for the first time an analytic expression for the two-loop amplitude for para-positronium decay to two photons at two loops., Comment: 34 pages, 6 figures, v2: references updated, version published in JHEP

\emph{Full-bond percolation} with parameter $p$ is the process in which, given a graph, for every edge independently, we delete the edge with probability $1-p$. Bond percolation is motivated by problems in mathematical physics and it is studied in parallel computing and network science to understand the resilience of distributed systems to random link failure and the spread of information in networks through unreliable links. Full-bond percolation is also equivalent to the \emph{Reed-Frost process}, a network version of \emph{SIR} epidemic spreading, in which the graph represents contacts among people and $p$ corresponds to the probability that a contact between an infected person and a susceptible one causes a transmission of the infection. We consider \emph{one-dimensional power-law small-world graphs} with parameter $\alpha$ obtained as the union of a cycle with additional long-range random edges: each pair of nodes $(u,v)$ at distance $L$ on the cycle is connected by a long-range edge $(u,v)$, with probability proportional to $1/L^\alpha$. Our analysis determines three phases for the percolation subgraph $G_p$ of the small-world graph, depending on the value of $\alpha$. 1) If $\alpha < 1$, there is a $p<1$ such that, with high probability, there are $\Omega(n)$ nodes that are reachable in $G_p$ from one another in $O(\log n)$ hops; 2) If $1 < \alpha < 2$, there is a $p<1$ such that, with high probability, there are $\Omega(n)$ nodes that are reachable in $G_p$ from one another in $\log^{O(1)}(n)$ hops; 3) If $\alpha > 2$, for every $p<1$, with high probability all connected components of $G_p$ have size $O(\log n)$. The setting of full-bond percolation in finite graphs studied in this paper, which is the one that corresponds to the network SIR model of epidemic spreading, had not been analyzed before.

We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals. We provide corrections up to $O(\epsilon^2)$ in the dimensional regulator for the first time which are relevant at NNLO. Four independent pentagon integral topologies appear in the complete description of the colour structure for which we provide numerical solutions using canonical form differential equations and the method of generalised power series expansions. Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation., Comment: 37 pages. ancillary files containing analytic amplitudes and integral evaluation routines. v2 references added. v3 fixing minor typos in the text and in the ancillary files

We characterized the light output response of a new 140 cm3 stilbene-d12 crystal up to 14.1 MeV neutron energies using a coincidence neutron scattering system. We also characterized its light output response to alpha particles in the 5 to 6~MeV energy range. The excellent PSD capability of the stilbene-d$_{12}$ detector allowed us to select light pulses produced by particles of increasing ionization density, namely electrons, protons, deuterium-ions, and alpha particles. The measured fast decay component of the light pulses is increasingly quenched as the ionization density of the particle in the crystal increases. Consistently with this finding, the Birks' quenching parameter of alpha particles is approximately 8.5 times larger compared to the quenching of deuterium ions, produced by neutron scattering interactions. The reported experimental characterization will allow high-fidelity modeling of the detector enabling its application for fast-neutron detection and spectroscopy in nuclear physics, radiation protection, nuclear security, and non-proliferation.

We report on the two-loop amplitude computation for the mixed QCD-electroweak corrections to the process $gg \to Hg$, with exact dependence on the electroweak boson masses. This amplitude has been employed in the computation of next-to-leading order (NLO) mixed QCD-electroweak corrections to the Higgs-boson production rate in arXiv:2010.09451. The master integrals that appear in the amplitude are evaluated by means of generalized power series expansions, which allows for fast and high-precision numerical evaluation of the amplitude in the physical phase-space, proving to be a powerful tool for phenomenological applications., Comment: 23 pages, 2 figures

We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) = -\frac{\gamma(g)}{\beta(g)} =\frac{\gamma_0}{\beta_0}\frac{1}{g} + \cdots $ determines which different cases of operator mixing can occur, and we review their classification. We derive a sufficient condition for $A(g)$ to be set in the one-loop exact form $A(g) = \frac{\gamma_0}{\beta_0}\frac{1}{g}$. Finally, we discuss the consequences of the unitarity requirement in massless QCD-like theories, and we demonstrate that $\gamma_0$ is always diagonalizable if the theory is conformal invariant and unitary in its free limit at $g =0$., Comment: 8 pages, fixed typo in the references. Contribution to the 15th International Symposium on Radiative Corrections (RADCOR) and the XIX Workshop on Radiative Corrections for the LHC and Future Colliders (LoopFest). arXiv admin note: substantial text overlap with arXiv:2103.16220

Background:Typically, proteins perform key biological functions by interacting with each other. As a consequence, predicting which protein pairs interact is a fundamental problem. Experimental methods are slow, expensive, and may be error prone.Many computational methods have been proposed to identify candidate interacting pairs. When accurate, they can serve as an inexpensive, preliminary filtering stage, to be followed by downstream experimental validation. Among such methods, sequence-based ones are very promising.Results:We present, a new algorithm that leverages both topological and biological information to predict protein-protein interactions. We comprehensively compare our Framework with state-of-the-art approaches on reliable PPIs datasets, showing that they have competitive or higher accuracy on biologically validated test sets.Conclusion:We shown that topological plus sequence-based computational methods can effectively predict the entire human interactome compared with methods that leverage only one source of biological information.

We have experimentally characterized the light-output response of a deuterated trans-stilbene (stilbene-d12) crystal to quasi-monoenergetic neutrons in the 0.8 to 4.4 MeV energy range. These data allowed us to perform neutron spectroscopy measurements of a DT 14.1 MeV source and a PuBe-239 source by unfolding the impinging neutron spectrum from the measured light-output response. The stilbene-d12 outperforms a H1-stilbene of similar size when comparing the shape of the unfolded spectra and the reference ones. These results confirm the viability of non-hygroscopic stilbene-d12 crystal for direct neutron spectroscopy without need for time-of-flight measurements. This capability makes stilbene-d12 a well suited detector for fast-neutron spectroscopy in many applications including nuclear reaction studies, radiation protection, nuclear non-proliferation, and space travel.

We work out the interplay between lowest-order perturbative computations in the 't Hooft coupling, $g^2=g^2_{YM} N$, operator mixing, renormalization-group (RG) improved ultraviolet (UV) asymptotics of leading-order (LO) nonplanar/planar contributions to $2$-point correlators, and nonperturbative large-$N$ expansion of perturbatively massless QCD-like theories. As concrete examples, we compute to the lowest perturbative order in $SU(N)$ YM theory the ratios, $r_i$, of LO-nonplanar to planar contributions to the $2$-point correlators in the orthogonal basis in the coordinate representation of the gauge-invariant dimension-$8$ scalar operators and all the twist-$2$ operators. We demonstrate that -- if $\frac{\gamma_0}{\beta_0}$ has no LO-nonplanar contribution, with $\gamma_0$ and $\beta_0$ the one-loop coefficients of the anomalous-dimension matrix and beta function respectively -- $r_i$ actually coincides with the corresponding ratio in the large-$N$ expansion of the RG-improved UV asymptotics of the $2$-point correlators, provided that a certain canonical nonresonant diagonal renormalization scheme exists for the corresponding operators. Contrary to the aforementioned scalar operators, for the first $10^3$ twist-$2$ operators we actually verify the above conditions, and we get the universal value $r_i=-\frac{1}{N^2}$. Hence, nonperturbatively such $r_i$ must coincide with the UV asymptotics of the ratio of the glueball self-energy loop to the glueball tree contribution to the $2$-point correlators above. As a consequence, the universality of $r_i$ reflects the universality of the effective coupling in the nonperturbative large-$N$ YM theory for the twist-$2$ operators in the coordinate representation., Comment: 24 pages, no figures

Recently, a geometric approach to operator mixing in massless QCD-like theories -- that involves canonical forms based on the Poincare'-Dulac theorem for the linear system that defines the renormalized mixing matrix in the coordinate representation $Z(x,\mu)$ -- has been advocated in arXiv:2103.15527 . As a consequence, a classification of operator mixing in four cases -- depending on the canonical forms of $- \frac{\gamma(g)}{\beta(g)}$, with $\gamma(g)=\gamma_0 g^2+\cdots$ the matrix of the anomalous dimensions and $\beta(g)=-\beta_0 g^3 + \cdots$ the beta function -- has been proposed: (I) nonresonant $\frac{\gamma_0}{\beta_0}$ diagonalizable, (II) resonant $\frac{\gamma_0}{\beta_0}$ diagonalizable, (III) nonresonant $\frac{\gamma_0}{\beta_0}$ nondiagonalizable, (IV) resonant $\frac{\gamma_0}{\beta_0}$ nondiagonalizable. In particular, in arXiv:2103.15527 a detailed analysis of the case (I) -- where operator mixing reduces to all orders of perturbation theory to the multiplicatively renormalizable case -- has been provided. In the present paper, following the aforementioned approach, we work out in the remaining three cases the canonical forms for $- \frac{\gamma(g)}{\beta(g)}$ to all orders of perturbation theory, the corresponding UV asymptotics of $Z(x,\mu)$, and the physics interpretation. We also work out in detail physical realizations of the cases (I) and (II)., Comment: 35 pages, formulas unchanged, but some comments on the UV asymptotics corrected, physical realizations of the resonant case and new references added

We obtain tight thresholds for bond percolation on one-dimensional small-world graphs, and apply such results to obtain tight thresholds for the \emph{Independent Cascade} process and the \emph{Reed-Frost} process in such graphs. These are the first fully rigorous results establishing a phase transition for bond percolation and SIR epidemic processes in small-world graphs. Although one-dimensional small-world graphs are an idealized and unrealistic network model, a number of realistic qualitative epidemiological phenomena emerge from our analysis, including the epidemic spread through a sequence of local outbreaks, the danger posed by random connections, and the effect of super-spreader events.