Miracle-dz/UniFAR-FTUs huggingface dataset:
Metric Geometry of Locally Compact Groups

This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous article. The theme has often been restricted to finitely generated groups, but it can favorably be played for locally compact groups. The development of the theory is illustrated by numerous examples, including matrix groups with entries in the the field of real or complex numbers, or other locally compact fields such as p-adic fields, isometry groups of various metric spaces, and, last but not least, discrete group themselves. Word metrics for compactly generated groups play a major role. In the particular case of finitely generated groups, they were introduced by Dehn around 1910 in connection with the Word Problem. Some of the results exposed concern general locally compact groups, such as criteria for the existence of compatible metrics on locally compact groups. Other results concern special classes of groups, for example those mapping onto the group of integers (the Bieri-Strebel splitting theorem for locally compact groups). Prior to their applications to groups, the basic notions of coarse and large-scale geometry are developed in the general framework of metric spaces. Coarse geometry is that part of geometry concerning properties of metric spaces that can be formulated in terms of large distances only. In particular coarse connectedness, coarse simple connectedness, metric coarse equivalences, and quasi-isometries of metric spaces are given special attention. The final chapters are devoted to the more restricted class of compactly presented groups, generalizing finitely presented groups to the locally compact setting. They can indeed be characterized as those compactly generated locally compact groups that are coarsely simply connected.
Poster: ReMouse Dataset: Measuring Similarity of Human-Generated Trajectories as an Important Step in Dealing with Session-Replay Bots

Session-replay bots are believed to be the latest and most advanced generation of web-bots, that are also difficult challenging to defend against. Combating session-replay bots is particularly problematic in online domains that get repeatedly visited by the same genuine human user(s), and possibly in the same/similar way - such as news, banking or gaming sites. Namely, in such domains, it is difficult to determine whether two look-alike sessions are produced by the same human user or these sessions are just bot-generated session replays. In this paper we introduce and provide to the public a novel real-world mouse dynamics dataset named ReMouse. ReMouse dataset is collected in a guided environment and, unlike other publicly available mouse dynamics dataset, it contains repeat-sessions generated by the same human user(s). As such, ReMouse dataset is first of its kind and is of particular relevance for studies on the development of effective defenses against session-replay bots. Our own statistical analysis of ReMouse dataset shows that not only two different human users are highly unlikely to generate same/similar looking sessions when performing the same/similar online task, but even the (repeat) sessions generated by the same human user are likely to be sufficiently distinguishable from one another.
DirtyCred: Escalating Privilege in Linux Kernel

The kernel vulnerability DirtyPipe was reported to be present in nearly all versions of Linux since 5.8. Using this vulnerability, a bad actor could fulfill privilege escalation without triggering existing kernel protection and exploit mitigation, making this vulnerability particularly disconcerting. However, the success of DirtyPipe exploitation heavily relies on this vulnerability's capability (i.e., injecting data into the arbitrary file through Linux's pipes). Such an ability is rarely seen for other kernel vulnerabilities, making the defense relatively easy. As long as Linux users eliminate the vulnerability, the system could be relatively secure. This work proposes a new exploitation method -- DirtyCred -- pushing other Linux kernel vulnerabilities to the level of DirtyPipe. Technically speaking, given a Linux kernel vulnerability, our exploitation method swaps unprivileged and privileged kernel credentials and thus provides the vulnerability with the DirtyPipe-like exploitability. With this exploitability, a bad actor could obtain the ability to escalate privilege and even escape the container. We evaluated this exploitation approach on 24 real-world kernel vulnerabilities in a fully-protected Linux system. We discovered that DirtyCred could demonstrate exploitability on 16 vulnerabilities, implying DirtyCred's security severity. Following the exploitability assessment, this work further proposes a new kernel defense mechanism. Unlike existing Linux kernel defenses, our new defense isolates kernel credential objects on non-overlapping memory regions based on their own privilege. Our experiment result shows that the new defense introduces primarily negligible overhead.
TChecker: Precise Static Inter-Procedural Analysis for Detecting Taint-Style Vulnerabilities in PHP Applications

PHP applications provide various interfaces for end-users to interact with on the Web. They thus are prone to taint-style vulnerabilities such as SQL injection and cross-site scripting. For its high efficiency, static taint analysis is widely adopted to detect taint-style vulnerabilities before application deployment. Unfortunately, due to the high complexity of the PHP language, implementing a precise static taint analysis is difficult. The existing taint analysis solutions suffer from both high false positives and high false negatives because of their incomprehensive inter-procedural analysis and a variety of implementation issues. In this work, we present TChecker, a context-sensitive inter-procedural static taint analysis tool to detect taint-style vulnerabilities in PHP applications. We identify that supporting objects and type systems is critical for statically analyzing programs written in the dynamic language PHP. We first carefully model the PHP objects and the related object-oriented programming features in TChecker. It then iteratively performs an inter-procedural data-flow analysis on PHP objects to refine object types, thus could precisely identify the call targets. We also take a considerable amount of effort in supporting other dynamic features of PHP such as dynamic includes. We comprehensively evaluated TChecker on a diverse set of modern PHP applications and demonstrated its high effectiveness in vulnerability detection. Specifically, TChecker successfully detected 18 previously unknown vulnerabilities in these PHP applications. We compared TChecker with the related static analysis tools and found that it significantly outperformed them by detecting more vulnerabilities. TChecker could also find all the vulnerabilities the existing tools detect with a relatively good precision. We release the source code of our prototype implementation to facilitate future research.
Quantum Riemann Surfaces in Chern-Simons Theory

We construct from first principles the operators $\hat A_M$ that annihilate the partition functions (or wavefunctions) of three-dimensional Chern-Simons theory with gauge groups $SU(2)$, $SL(2,\mathbb{R})$, or $SL(2,\mathbb{C})$ on knot complements $M$. The operator $\hat A_M$ is a quantization of a knot complement's classical $A$-polynomial $A_M(\ell,m)$. The construction proceeds by decomposing three-manifolds into ideal tetrahedra, and invoking a new, more global understanding of gluing in topological quantum field theory to put them back together. We advocate in particular that, properly interpreted, 'gluing $=$ symplectic reduction. ' We also arrive at a new finite-dimensional state integral model for computing the analytically continued 'holomorphic blocks' that compose any physical Chern-Simons partition function.
Lens surgeries along the $n$-twisted Whitehead link

We determine lens surgeries (i.e.\ Dehn surgery yielding a lens space) along the $n$-twisted Whitehead link. To do so, we first give necessary conditions to yield a lens space from the Alexander polynomial of the link as: (1) $n=1$ (i.e. the Whitehead link), and (2) one of surgery coefficients is 1, 2 or 3. Our interests are not only lens surgery itself but also how to apply the Alexander polynomial for this kind of problems.
Markov branching in the vertex splitting model

We study a special case of the vertex splitting model which is a recent model of randomly growing trees. For any finite maximum vertex degree D, we find a one parameter model, with parameter which has a so-called Markov branching property. When we find a two parameter model with an additional parameter which also has this feature. In the case D = 3, the model bears resemblance to Ford’s α-model of phylogenetic trees and when it is similar to its generalization, the αγ-model. For α = 0, the model reduces to the well known model of preferential attachment. In the case α > 0, we prove convergence of the finite volume probability measures, generated by the growth rules, to a measure on infinite trees which is concentrated on the set of trees with a single spine. We show that the annealed Hausdorff dimension with respect to the infinite volume measure is 1/α. When γ = 0 the model reduces to a model of growing caterpillar graphs in which case we prove that the Hausdorff dimension is almost surely 1/α and that the spectral dimension is almost surely 2/(1 + α). We comment briefly on the distribution of vertex degrees and correlations between degrees of neighbouring vertices.
Kulikov surfaces form a connected component of the moduli space

Abstract We show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type with pg = 0 and K 2 = 6. We also give a new description for these surfaces, extending ideas of Inoue. Finally, we calculate the bicanonical degree of Kulikov surfaces and prove that they verify the Bloch conjecture.
State-relevant Maxwell's equation from Kaluza-Klein theory

We study a five-dimensional perfect fluid coupled with Kaluza-Klein gravity. By dimensional reduction, a modified form of Maxwell's equation is obtained, which is relevant to the equation of state of the source. Since the relativistic magnetohydrodynamics and the three-dimensional formulation are widely used to study space matter, we derive the modified Maxwell's equations and relativistic magnetohydrodynamics in 3+1 form. We then take an ideal Fermi gas as an example to study the modified effect, which can be visible under high-density or high-energy conditions, while the traditional Maxwell's equation can be regarded as a result in the low density and low temperature limit. We also indicate the possibility to test the state-relevant effect of Kaluza-Klein theory in a telluric laboratory.
Phylogenetic analysis of the MCL1 BH3 binding groove and rBH3 sequence motifs in the p53 and INK4 protein families

B-cell lymphoma 2 (Bcl-2) proteins are central, conserved regulators of apoptosis. Bcl-2 family function is regulated by binding interactions between the Bcl-2 homology 3 (BH3) motif in pro-apoptotic family members and the BH3 binding groove found in both the pro-apoptotic effector and anti-apoptotic Bcl-2 family members. A novel motif, the reverse BH3 (rBH3), has been shown to interact with the anti-apoptotic Bcl-2 homolog MCL1 (Myeloid cell leukemia 1) and have been identified in the p53 homolog p73, and the CDK4/6 (cyclin dependent kinase 4/6) inhibitor p18INK4c, (p18, cyclin-dependent kinase 4 inhibitor c). To determine the conservation of rBH3 motif, we first assessed conservation of MCL1’s BH3 binding groove, where the motif binds. We then constructed neighbor-joining phylogenetic trees of the INK4 and p53 protein families and analyzed sequence conservation using sequence logos of the rBH3 locus. This showed the rBH3 motif is conserved throughout jawed vertebrates p63 and p73 sequences and in chondrichthyans, amphibians, mammals, and some reptiles in p18. Finally, a potential rBH3 motif was identified in mammalian and osteichthyan p19INK4d (p19, cyclin dependent kinase 4 inhibitor d). These findings demonstrate that the interaction between MCL1 and other cellular proteins mediated by the rBH3 motif may be conserved throughout jawed vertebrates.
Nonabelian cohomology jump loci from an analytic viewpoint

For a space, we investigate its CJL (cohomology jump loci), sitting inside varieties of representations of the fundamental group. To do this, for a CDG (commutative differential graded) algebra, we define its CJL, sitting inside varieties of flat connections. The analytic germs at the origin 1 of representation varieties are shown to be determined by the Sullivan 1-minimal model of the space. Up to a degree q, the two types of CJL have the same analytic germs at the origins, when the space and the algebra have the same q-minimal model. We apply this general approach to formal spaces (obtaining the degeneration of the Farber–Novikov spectral sequence), quasi-projective manifolds, and finitely generated nilpotent groups. When the CDG algebra has positive weights, we elucidate some of the structure of (rank one complex) topological and algebraic CJL: all their irreducible components passing through the origin are connected affine subtori, respectively rational linear subspaces. Furthermore, the global exponential map sends all algebraic CJL into their topological counterpart.
Invariant Gaussian fields on homogeneous spaces: explicit constructions and mean nodal volume

— We review and study some of the properties of smooth Gaussian random ﬁelds deﬁned on a homogeneous space, under the assumption that the probability distribution is invariant under the isometry group of the space. We ﬁrst give an exposition, building on early results of Yaglom, of the way in which representation theory and the associated special functions make it possible to give completely explicit descriptions of these ﬁelds in many cases of interest. We then turn to the expected size of the zero-set: extending two-dimensional results from Optics and Neuroscience, we show that every invariant ﬁeld comes with a natural unit of volume (deﬁned in terms of the geometrical redundancies in the ﬁeld) with respect to which the average size of the zero-set is given by a universal constant depending only on the dimension of the source and target spaces, and not on the precise symmetry exhibited by the ﬁeld.
Reducing systems for very small trees

We study very small trees from the point of view of reducing systems of free factors, which are analogues of reducing systems of curves for a surface lamination; a non-trivial, proper free factor $F \leq \FN$ reduces $T$ if and only if $F$ acts on some subtree of $T$ with dense orbits. We characterize those trees, called arational, which do not admit a reduction by any free factor: $T$ is arational if and only if either $T$ is free and indecomposable or $T$ is dual to a surface with one boundary component equipped with an arational measured foliation. To complement this result, we establish some results giving control over the collection of all factors reducing a given tree. As an application, we deduce a form of the celebrated Bestvina-Handel classification theorem for elements of $Out(\FN)$. We also include an appendix containing examples of very small trees. The results of this paper are used in Bestvina and Reynolds (2012), where we describe the Gromov boundary of the complex of free factors.
Inclusion or exclusion: Language ideology and language-in-education policies in Pakistan

Abstract:The choice of a medium of instruction (MoI) is an ideological construct, closely linked to language, ideology and power. The Urdu/English-medium divide in Pakistan has reframed the ideologies in a way that a large majority of the rural population has become status conscious. English-Medium Instruction (EMI) policy has been used as a lens to examine parental ideologies of dropped-out children in language choice as MoI and to observe the gap between actual language policy and practices. Building on Spolsky's (2004) Language Policy Model, a framework has been explicated to analyse the ideological change in the context of language choice with reference to EMI. Results suggest that the policy and practice gap concerning English has proven to be a tool of exclusion rather than inclusion for the masses and thus poor parents idealise English-medium schooling as the only option for a better future for their children, or otherwise pushing them out of public schools. This research, therefore, argues that in order to ensure inclusion, language-in-education policy needs to be revisited on the principles of equity and impartiality so that it can win parents' trust. Résumé:Le choix d'un moyen d'instruction est une construction idéologique, étroitement liée à la langue, à l'idéologie et au pouvoir. La fracture entre l'ourdou et l'anglais au Pakistan a recadré les idéologies d'une manière telle qu'une grande majorité de la population rurale est devenue consciente de son statut. La politique de l'anglais comme moyen d'instruction a été utilisée comme lentille pour examiner les idéologies parentales des enfants déscolarisés dans le choix de la langue en tant que moyen d'instruction, et pour observer l'écart entre la politique et les pratiques linguistiques réelles. S'appuyant sur le modèle de politique linguistique de , un cadre a été expliqué pour analyser le changement idéologique dans le contexte du choix de la langue en référence à l'enseignement en anglais. Les résultats suggèrent que l'écart entre les politiques et les pratiques concernant l'anglais s'est avéré être un outil d'exclusion plutôt que d'inclusion pour les masses, et donc les parents pauvres idéalisent la scolarisation en anglais comme la seule option pour un meilleur avenir pour leurs enfants, l'alternative étant de les retirer des écoles publiques. Cette recherche soutient donc qu'afin d'assurer l'inclusion, la politique de langue dans l'éducation doit être revue sur les principes d'équité et d'impartialité afin qu'elle puisse gagner la confiance des parents.
On Hilbert Covariants

Abstract Let $F$ denote a binary form of order $d$ over the complex numbers. If $r$ is a divisor of $d$ , then the Hilbert covariant ${{H}_{r,\,d}}\,\left( F \right)$ vanishes exactly when $F$ is the perfect power of an order $r$ form. In geometric terms, the coefficients of $H$ give defining equations for the image variety $X$ of an embedding ${{\text{P}}^{r}}\,\to \,{{\text{P}}^{d}}$ . In this paper we describe a new construction of the Hilbert covariant and simultaneously situate it into a wider class of covariants called the Göttingen covariants, all of which vanish on $X$ . We prove that the ideal generated by the coefficients of $H$ defines $X$ as a scheme. Finally, we exhibit a generalisation of the Göttingen covariants to $n$ -ary forms using the classical Clebsch transfer principle.
Convergence in distribution for filtering processes associated to Hidden Markov Models with densities

A Hidden Markov Model generates two basic stochastic processes, a Markov chain, which is hidden, and an observation sequence. The filtering process of a Hidden Markov Model is, roughly speaking, the sequence of conditional distributions of the hidden Markov chain that is obtained as new observations are received.It is well-known, that the filtering process itself, is also a Markov chain. A classical, theoretical problem is to find conditions which implies that the distributions of the filtering process converge towards a unique limit measure.This problem goes back to a paper of D Blackwell for the case when the Markov chain takes its values in a finite set and it goes back to a paper of H Kunita for the case when the state space of the Markov chain is a compact Hausdor space.Recently, due to work by F Kochmann, J Reeds, P Chigansky and R van Handel, a necessary and sucient condition for the convergence of the distributions of the filtering process has been found for the case when the state space is finite. This condition has since been generalised to the case when the state space is denumerable.In this paper we generalise some of the previous results on convergence in distribution to the case when the Markov chain and the observation sequence of a Hidden Markov Model take their values in complete, separable, metric spaces; it has though been necessary to assume that both the transition probability function of the Markov chain and the transition probability function that generates the observation sequence have densities.
Primordial density perturbations and reheating from gravity

We consider the presence and evolution of primordial density perturbations in a cosmological model based on a simple ansatz which captures--by providing a set of effective gravitational field equations--the strength of the enhanced quantum loop effects that can arise during inflation. After deriving the general equations that perturbations obey, we concentrate on scalar perturbations and show that their evolution is quite different than that of conventional inflationary models but still phenomenologically acceptable. The main reason for this novel evolution is the presence of an oscillating regime after the end of inflation which makes all superhorizon scalar modes oscillate. The same reason allows for a natural and very fast reheating mechanism for the Universe.
Extensions of a class of similarity solutions of Fokker-Planck equation with time-dependent coefficients and fixed/moving boundaries

A general formula in closed form to obtain exact similarity solutions of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients was recently presented by Lin and Ho [ Ann. Phys. \textbf{327}, 386 (2012); J. Math. Phys. \textbf{54}, 041501 (2013)]. In this paper we extend the class of exact solutions by exploiting certain properties of the general formula.
Intersections of sets, diophantine equations and Fourier analysis

A classical theorem due to Mattila (see \cite{Mat84}; see also \cite{M95}, Chapter 13) says that if $A,B \subset {\Bbb R}^d$ of Hausdorff dimension $s_A, s_B$, respectively, with $s_A+s_B \ge d$, $s_B>\frac{d+1}{2}$ and $dim_{{\mathcal H}}(A \times B)=s_A+s_B\ge d$, then $$ dim_{{\mathcal H}}(A \cap (z+B)) \leq s_A+s_B-d$$ for almost every $z \in {\Bbb R}^d$, in the sense of Lebesgue measure. In this paper, we replace the Hausdorff dimension on the left hand side of the first inequality above by the upper Minkowski dimension, replace the Lebesgue measure of the set of translates by a Hausdorff measure on a set of sufficiently large dimension and replace the translation and rotation group by a more general variable coefficient family of transformations. Interesting arithmetic issues arise in the consideration of sharpness examples. These results are partly motivated by those in \cite{EIT11} and \cite{IJL10} where in the former the classical regular value theorem from differential geometry was investigated in a fractal setting and in the latter discrete incidence theory is explored from an analytic standpoint. Fourier Integral Operator bounds and other techniques of harmonic analysis play a crucial role in our investigation. We also consider, in the spirit of the Furstenberg conjecture, inverse problems for intersections by asking how small a dimension of a set can be given that the dimension of its intersections with a suitably well-curved family of manifolds is bounded from below by a given threshold. Finally, we shall discuss applications of our estimates to the problem of estimating the number of solutions of systems of diophantine equations over integers.