Partition games

We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can perform on a single heap. In normal play, the player with the last move wins, and the famous Sprague-Grundy theory provides a solution. We prove that several rulesets have a periodic or an arithmetic periodic Sprague-Grundy sequence (i.e. they can be partitioned into a finite number of arithmetic progressions of the same common difference). This is achieved directly for some infinite classes of games, and moreover we develop a computational testing condition, demonstrated to solve a variety of additional games. Similar results have previously appeared for various classes of games of take-and-break, for example octal and hexadecimal; see e.g. Winning Ways by Berlekamp, Conway and Guy (1982). In this context, our contribution consists of a systematic study of the subclass `break-without-take'

A Review of Formal Methods applied to Machine Learning

We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability of mature tools, their use is well established in the industry, and in particular to check safety-critical applications as they undergo a stringent certification process. As machine learning is becoming more popular, machine-learned components are now considered for inclusion in critical systems. This raises the question of their safety and their verification. Yet, established formal methods are limited to classic, i.e. non machine-learned software. Applying formal methods to verify systems that include machine learning has only been considered recently and poses novel challenges in soundness, precision, and scalability. We first recall established formal methods and their current use in an exemplar safety-critical field, avionic software, with a focus on abstract interpretation based techniques as they provide a high level of scalability. This provides a golden standard and sets high expectations for machine learning verification. We then provide a comprehensive and detailed review of the formal methods developed so far for machine learning, highlighting their strengths and limitations. The large majority of them verify trained neural networks and employ either SMT, optimization, or abstract interpretation techniques. We also discuss methods for support vector machines and decision tree ensembles, as well as methods targeting training and data preparation, which are critical but often neglected aspects of machine learning. Finally, we offer perspectives for future research directions towards the formal verification of machine learning systems

Share \& Shrink: (In-)Feasibility of MPC from one Broadcast-then-Asynchrony, and Improved Complexity

We consider protocols for secure multi-party computation (MPC) under honest majority, i.e., for $N=2t+1$ players of which $t$ are corrupt, that achieve guaranteed output delivery (GOD), and which operate in $1$ single initial round of broadcast (BC), followed by some steps of asynchronous peer-to-peer (P2P) messages. The power of closely related ``hybrid networks\u27\u27 was studied in [Fitzi-Nielsen, Disc\u2709], [Beerliova-Hirt-Nielsen, Podc\u2710], [Patra-Ravi, IEEE Trans. Inf. Theory\u2718] and [Choudhury, Podc\u2720]. Interest of such protocols is that they go at the actual speed of the network, and their security is preserved under arbitrary network conditions (past the initial broadcast). We first complete the picture of this model with an impossibility result showing that some setup is required to achieve honest majority MPC with GOD. We then consider a bare bulletin-board PKI setup, and leverage recent advances on multi-key fully homomorphic encryption [BJMS, Asiacrypt\u2720], to state feasibility of MPC in a tight 1 BC then 1 single step of asynchronous P2P. We then consider efficiency. The only protocols which can be adapted to tolerate such network model and setup are [Gordon-Liu-Shi, Crypto\u2715] and [BJMS, Asiacrypt\u2720]. The former does not allow inputs from external lightweight owners and is inherently limited to the GSW FHE, while the sizes of the ciphertexts of the latter are quadratic in the number of input owners. Our main contribution is a very simple and generic design which enables MPC in 1BC-then-asynchronous P2P. It operates over ciphertexts encrypted over a (threshold) single-key encryption scheme. Hence, they have the smallest sizes expectable. It operates from any public key encryption scheme with a key generation, encryption and decryption which are built from linear maps (such as GSW, BFV, CL). Our main building block is the squishing in the BC of both the publicly verifiable sharing of the inputs (``Share\u27\u27), in parallel with distributed key generation (DKG), then followed by threshold encryption (``Shrink\u27\u27) in one step of asynchronous P2P. As a bonus, this design allows inputs from possibly lightweight external owners. We then aim at instantiating the design from the BFV FHE, but surprisingly there exists no robust threshold BFV scheme. Precisely, all existing protocols for generating a common relinearisation key can abort as soon as one player deviates. We solve this issue, with a relinearisation key (adapted from [CDKS, CCS\u2719]) which we show how to securely generate in parallel of the threshold key, in the same broadcast. We thus obtain the first robust threshold BFV. We believe that this contribution is of independent interest. Of independent interest, as an optional alternative, we propose the first threshold FHE decryption enabling simultaneously: (i) robustness under asynchrony with honest majority; (ii) tolerating a power-of-small-prime ciphertext modulus, e.g., $2^e$; and (iii) secret shares of sizes quasi-independent of $N$

Breaking the t<n/3t< n/3 Consensus Bound: Asynchronous Dynamic Proactive Secret Sharing under Honest Majority

A proactive secret sharing scheme (PSS), expressed in the dynamic-membership setting, enables a committee of n holders of secret-shares, dubbed as players, to securely hand-over new shares of the same secret to a new committee. We dub such a sub-protocol as a Refresh. All existing PSS under an honest majority, require the use of a broadcast (BC) in each refresh. BC is costly to implement, and its security relies on timing assumptions on the network. So the privacy of the secret and/or its guaranteed delivery, either depend on network assumptions, or, on the reliability of a public ledger. By contrast, PSS over asynchronous channels do not have these constraints. However, all of them (but one, with exponential complexity) use asynchronous verifiable secret sharing (AVSS) and consensus (MVBA and/or ACS), which are impossible under asynchrony beyond t<n/3 corruptions, whatever the setup. We present a PSS, named asynchronous-proactive secret sharing (APSS), which is the first PSS under honest majority with guaranteed output delivery in a completely asynchronous network. More generally, APSS allows any flexible threshold $t<n$, such that privacy and correctness are guaranteed up to t corruptions, and liveness as soon as $t+1$ players behave honestly. Correctness can be lifted to any number of corruptions, provided a linearly homomorphic commitment scheme. Moreover, each refresh completes at the record speed of $2\delta$, where $\delta$ is the actual message delivery delay. APSS demonstrates that proactive refreshes are possible as long as players of the initial committee only, have a common view on a set of (publicly committed or encrypted) shares. Despite not providing consensus on a unique set of shares, APSS surprisingly enables the opening of any linear map over secrets { non-interactively, without consensus }. This, in turn, applies to threshold signing, decryption and randomness generation. APSS can also be directly integrated into the asynchronous Schnorr threshold signing scheme Roast [CCS\u2722]. Of independent interest, we: - provide the first UC formalization (and proof) of proactive AVSS, furthermore for arbitrary thresholds; - provide additional mechanisms enabling players of a committee to start a refresh then erase their old shares, synchronously up to $\delta$ from each other; - improve by 50x the verification speed of the NIZKs of encrypted re-sharing of [Cascudo et al, Asiacrypt\u2722], by using novel optimizations of batch Schnorr proofs of knowledge. We demonstrate efficiency of APSS with an implementation which uses this optimization as baseline

Comment des parents d’élèves et des enseignants spécialisés voient la réussite et la difficulté scolaires

L’objectif de cette étude est d’explorer la manière dont des acteurs du système scolaire profanes (parents d’élèves) ou experts (enseignants spécialisés) se représentent l’élève en réussite scolaire et l’élève en difficulté scolaire. Pour ce faire, nous avons interrogé 29 parents d’élèves et 33 enseignants spécialisés. Les résultats indiquent que la représentation de la difficulté se décompose en trois catégories (environnement, caractéristiques personnelles et culture), alors que celle de la réussite se compose de deux catégories (environnement et caractéristiques personnelles). Les autres résultats montrent que la représentation d’un élève en difficulté scolaire n’est pas l’inverse de celle d’un élève en réussite, et que les causes évoquées pour expliquer ces statuts ne sont pas non plus opposées. Enfin la représentation des parents et des enseignants spécialisés diffèrent globalement, avec notamment une homogénéité et un consensus plus grands dans la représentation de ces derniers.The purpose of this study is to look closely at the way people within the school system–uninitiated (parents) or expert (special education teachers)–see successful students and those having learning difficulties. To do so we have questioned 29 parents and 33 special education teachers. The results show that in those people’s minds, difficulties are sorted out into three categories: backgrounds, personal and cultural features whereas success is divided into two categories: backgrounds, and personal features. Other results show that the mental representation that people have of a child with learning difficulties is not the opposite of that of a successful one, and the reasons given to explain these phenomena are not opposed either. Finally the parents’ and teachers’ mental representations are on the whole rather different, with, for instance, better homogeneity and wider consensus in teachers.El objetivo de este estudio estriba en explorar cómo actores profanos del sistema escolar (padres de alumnos) o expertos (docentes especializados) se representan al alumno en situación de éxito escolar y al alumno con dificultades escolares. Para ello, interrogamos a 29 padres de alumnos y a 33 docentes especializados. Los resultados indican que la representación de las dificultades se descompone en tres categorías (entorno, características personales y cultura), mientras el éxito se compone de dos categorías (entorno y características personales). Los otros resultados muestran que la representación de un alumno con dificultades escolares no es inversa a la de un alumno que conoce el éxito escolar, y que los motivos mencionados para explicar esos estatus tampoco se oponen. Por fin, la representación de los padres y de los docentes especializados difiere globalmente, en particular con una homogeneidad y un consenso más importantes en la representación de los docentes.Das Ziel dieser Studie ist, die Art und Weise zu beobachten, wie Laien (Eltern) oder Profis (Sonderschullehrer) im Schulsystem sich den erfolgreichen Schüler und den Schüler mit Schwierigkeiten vorstellen. Zu diesem Zweck haben wir 29 Eltern und 33 Sonderschullehrer befragt. Die Ergebnisse zeigen, dass die Vorstellung der Schwierigkeit sich in drei Kategorien gliedert (Umfeld, persönliche Merkmale und Kultur), während der Erfolg aus zwei Kategorien besteht (Umfeld und persönliche Merkmale). Die übrigen Ergebnisse zeigen, dass die Vorstellung eines Schülers mit Schwierigkeiten nicht das genaue Gegenteil von der eines erfolgreichen Schülers ist, und dass die Gründe, die diese beiden Status erklären können auch nicht entgegengesetzt sind. Zum Schluss unterscheiden sich insgesamt die Vorstellungen der Eltern und die der Sonderschullehrer, insbesondere mit größerer Homogenität und größerem Konsens in den Vorstellungen der Lehrer

Stéréotypes de la difficulté scolaire : un outil de recueil

Les recherches actuelles dans le domaine de l’éducation attestent de l’influence des stéréotypes sociaux sur les résultats académiques des élèves. Afin de connaître les stéréotypes liés aux « élèves en difficulté scolaire » au cycle 3, nous avons construit un outil auprès de psychologues scolaires, d’étudiants, de parents d’élèves, d’élèves de cycle 3, d’enseignants spécialisés et de stagiaires professeurs des écoles (PE2). L’analyse a permis d’obtenir quarante-neuf traits généraux mais aussi spécifiques aux groupes interrogés. Différentes méthodologies permettant de mesurer les stéréotypes avec cet outil sont présentées en discussion.Current research in the field of education shows the effects of social stereotypes on students’ academic performances. To determine the stereotypes of “5th grade students having learning disabilities”, we built an instrument with a sample of educational psychologists, undergraduate students, 5th grade students’ parents, 5th grade students, specialised teachers, and student teachers. Forty-nine traits that are general and sometimes specific to the respondent groups were obtained. The discussion section presents different ways to measure these stereotypes using this instrument

Adhesion of Plasmodium falciparum-infected erythrocytes to human cells: molecular mechanisms and therapeutic implications

Severe malaria has a high mortality rate (15–20%) despite treatment with effective antimalarial drugs. Adjunctive therapies for severe malaria that target the underlying disease process are therefore urgently required. Adhesion of erythrocytes infected with Plasmodium falciparum to human cells has a key role in the pathogenesis of life-threatening malaria and could be targeted with antiadhesion therapy. Parasite adhesion interactions include binding to endothelial cells (cytoadherence), rosetting with uninfected erythrocytes and platelet-mediated clumping of infected erythrocytes. Recent research has started to define the molecular mechanisms of parasite adhesion, and antiadhesion therapies are being explored. However, many fundamental questions regarding the role of parasite adhesion in severe malaria remain unanswered. There is strong evidence that rosetting contributes to severe malaria in sub-Saharan Africa; however, the identity of other parasite adhesion phenotypes that are implicated in disease pathogenesis remains unclear. In addition, the possibility of geographic variation in adhesion phenotypes causing severe malaria, linked to differences in malaria transmission levels and host immunity, has been neglected. Further research is needed to realise the untapped potential of antiadhesion adjunctive therapies, which could revolutionise the treatment of severe malaria and reduce the high mortality rate of the disease