Contribution of Jonas Kubilius to the metric theory of Diophantine approximation of dependent variables

The article is devoted to the latest results in metric theory of Diophantine approximation. One of the first major result in area of number theory was a theorem by academician Jonas Kubilius. This paper is dedicated to centenary of his birth. Over the last 70 years, the area of Diophantine approximation yielded a number of significant results by great mathematicians, including Fields prize winners Alan Baker and Grigori Margulis. In 1964 academician of the Academy of Sciences of BSSR Vladimir Sprindžuk, who was a pupil of academician J. Kubilius, solved the well-known Mahler’s conjecture on the measure of the set of S-numbers under Mahler’s classification, thus becoming the founder of the Belarusian academic school of number theory in 1962.

Diving Deep into the Weak Keys of Round Reduced Ascon

At ToSC 2021, Rohit et al. presented the first distinguishing and key recovery attacks on 7 rounds Ascon without violating the designer’s security claims of nonce-respecting setting and data limit of 264 blocks per key. So far, these are the best attacks on 7 rounds Ascon. However, the distinguishers require (impractical) 260 data while the data complexity of key recovery attacks exactly equals 264. Whether there are any practical distinguishers and key recovery attacks (with data less than 264) on 7 rounds Ascon is still an open problem.In this work, we give positive answers to these questions by providing a comprehensive security analysis of Ascon in the weak key setting. Our first major result is the 7-round cube distinguishers with complexities 246 and 233 which work for 282 and 263 keys, respectively. Notably, we show that such weak keys exist for any choice (out of 64) of 46 and 33 specifically chosen nonce variables. In addition, we improve the data complexities of existing distinguishers for 5, 6 and 7 rounds by a factor of 28, 216 and 227, respectively. Our second contribution is a new theoretical framework for weak keys of Ascon which is solely based on the algebraic degree. Based on our construction, we identify 2127.99, 2127.97 and 2116.34 weak keys (out of 2128) for 5, 6 and 7 rounds, respectively. Next, we present two key recovery attacks on 7 rounds with different attack complexities. The best attack can recover the secret key with 263 data, 269 bits of memory and 2115.2 time. Our attacks are far from threatening the security of full 12 rounds Ascon, but we expect that they provide new insights into Ascon’s security.

Approximating Geometric Knapsack via L-packings

We study the two-dimensional geometric knapsack problem, in which we are given a set of n axis-aligned rectangular items, each one with an associated profit, and an axis-aligned square knapsack. The goal is to find a (non-overlapping) packing of a maximum profit subset of items inside the knapsack (without rotating items). The best-known polynomial-time approximation factor for this problem (even just in the cardinality case) is 2+ε [Jansen and Zhang, SODA 2004]. In this article we present a polynomial-time 17/9+ε < 1.89-approximation, which improves to 558/325+ε < 1.72 in the cardinality case. Prior results pack items into a constant number of rectangular containers that are filled via greedy strategies. We deviate from this setting and show that there exists a large profit solution where items are packed into a constant number of containers plus one L-shaped region at the boundary of the knapsack containing narrow-high items and thin-wide items. These items may interact in complex manners at the corner of the L. The best-known approximation ratio for the subproblem in the L-shaped region is 2+ε (via a trivial reduction to one-dimensional knapsack); hence, as a second major result we present a PTAS for this case that we believe might be of broader utility. We also consider the variant with rotations, where items can be rotated by 90 degrees. Again, the best-known polynomial-time approximation factor (even for the cardinality case) is 2+ε [Jansen and Zhang, SODA 2004]. We present a polynomial-time (3/2+ε)-approximation for this setting, which improves to 4/3+ε in the cardinality case.

The Battle of Helena, the Little Rock Campaign, and the Capture of Fort Smith, 1863

The Battle of Helena, the Little Rock Campaign, and the capture of Fort Smith led to Union control over the Arkansas River Valley and most of Arkansas to the north of the river. Militarily this resulted in impeding Confederate operations in Missouri, the establishment of a potential base of operations for Union campaigns in Texas, and easier logistical support for Union forces in Indian Territory. A major result of these movements was the emancipation of thousands of slaves. Politically they brought a restoration of a pro-Union government in Arkansas. The occupation of Little Rock produced renewed economic prosperity and, under the benevolent policies of Union Maj. Gen. Frederick Steele, a return of normal social activity among the civilian population, though producing privation and disruption of gender and age roles in the surrounding countryside.

High throughput accurate method for estimating in vitro dry matter digestibility of maize silage

Background Since the introduction of studies on maize silage digestibility at the end of the nineteenth century, protocols to estimate dry matter digestibility have not stopped evolving. Since the early 1980s, the protocol developed by Aufrère became a benchmark in many laboratories to estimate in vitro dry matter digestibility. In order to increase its throughput, to facilitate its execution and to decipher the impact of the different parameters of the protocol we decided to test the combination of 7 parameters in 21 different protocols. Results We thus tested the impact of (1) the presence or absence of pepsin in HCl solution, (2) the temperature of incubation during enzymatic hydrolysis, (3) the presence or absence of a gelatinization step, (4) washing/rinsing versus neutralization step, (5) the presence or absence of α-amyloglucosidase in enzymatic solution, (6) the duration of cellulase incubation, and (7) the concentration of the cellulase solution. The major result of our work highlighted that it was essential to carry out a gelatinization step to correctly estimate the in vitro dry matter digestibility of maize silage. Conclusions The proposed protocol in this paper is innovative, reliable, highthroughput and easy to implement in many laboratories to accurately quantity in vitro dry matter digestibility.

Platform Competition with Multihoming on Both Sides: Subsidize or Not?

A major result in the study of two-sided platforms is the strategic interdependence between the two sides of the same platform, leading to the implication that a platform can maximize its total profits by subsidizing one of its sides. We show that this result largely depends on assuming that at least one side of the market single-homes. As technology makes joining multiple platforms easier, we increasingly observe that participants on both sides of two-sided platforms multihome. The case of multihoming on both sides is mostly ignored in the literature on competition between two-sided platforms. We help to fill this gap by developing a model for platform competition in a differentiated setting (a Hotelling line), which is similar to other models in the literature but focuses on the case where at least some agents on each side multihome. We show that when both sides in a platform market multihome, the strategic interdependence between the two sides of the same platform will diminish or even disappear. Our analysis suggests that the common strategic advice to subsidize one side in order to maximize total profits may be limited or even incorrect when both sides multihome, which is an important caveat given the increasing prevalence of multihoming in platform markets. This paper was accepted by Joshua Gans, business strategy.

Can neutron disappearance/reappearance experiments definitively rule out the existence of hidden braneworlds endowed with a copy of the Standard Model?

Many works, aiming to explain the origin of dark matter or dark energy, consider the existence of hidden (brane)worlds parallel to our own visible world — our usual Universe — in a multidimensional bulk. Hidden braneworlds allow for hidden copies of the Standard Model. For instance, atoms hidden in a hidden brane could exist as dark matter candidates. As a way to constrain such hypotheses, the possibility for neutron–hidden neutron swapping can be tested thanks to disappearance-reappearance experiments also known as passing-through-walls neutron experiments. The neutron-hidden neutron coupling [Formula: see text] can be constrained from those experiments. While [Formula: see text] could be arbitrarily small, previous works involving a [Formula: see text] bulk, with DGP branes, show that [Formula: see text] then possesses a value which is reachable experimentally. It is of crucial interest to know if a reachable value for [Formula: see text] is universal or not and to estimate its magnitude. Indeed, it would allow, in a near future, to reject definitively — or not — the existence of hidden braneworlds from experiments. In the present paper, we explore this issue by calculating [Formula: see text] for DGP branes, for [Formula: see text], [Formula: see text] and [Formula: see text] bulks. As a major result, no disappearance-reappearance experiment would definitively universally rules out the existence of hidden worlds endowed with their own copy of Standard Model particles, except for specific scenarios with conditions reachable in future experiments.

Analysis of Factors that Tourists Attach Importance to Rural Tourism Image——Taking Rural Tourism in Ningde Region as Example

Rural tourism was formed with traditional characteristics of the countryside industry naturally. It combined with human ecology, production, and ecological environment. In order to prepare the image of the future shape of rural tourism strategy in Ningde regions. This study classified visitors' importance of image of rural tourism into 6 categories: "leisure recreation", "improving knowledge", "service facilities", "modern function", "childhood in the countryside", and "rich theme activities" by using factor analysis and structured questionnaires to a random sample survey for the visitors over 15 years old. The major result was summarized as follows: the research shows that there are significant differences in tourists' views on the importance of rural tourism image at all levels, and the most importance image of visitors to rural tourism was "service facilities".

Variational Method to p-Laplacian Fractional Dirichlet Problem with Instantaneous and Noninstantaneous Impulses

In this paper, a research has been done about the existence of solutions to the Dirichlet boundary value problem for p-Laplacian fractional differential equations which include instantaneous and noninstantaneous impulses. Based on the critical point principle and variational method, we provide the equivalence between the classical and weak solutions of the problem, and the existence results of classical solution for our equations are established. Finally, an example is given to illustrate the major result.

Khamsin: A New Vision for the Middle East

This chapter explores the history of the journal Khamsin. Revue des socialistes révolutionnaires du Proche-Orient. The chapter demonstrates how the language of progress, socialism, and revolution provided the basis for cooperation between Jewish-Israeli and Arab intellectuals throughout the Middle East of the 1970s. The publication of Khamsin, which was founded in 1975 and published until 1987, was one major result of this cooperation. First the biography of Matzpen’s Eli Lobel is outlined, who was known for his unparalleled support for post-colonial states in Asia and Africa but who was also the guiding spirit behind Khamsin. Proceeding from the biographies of Leila S. Kadi, Sadik J. Al-Azm and Lafif Lakhdar, the chapter sketches in the experiences of a generation of the Arab Left that, after the defeat of June 1967, voiced a radical self-critique of the Arab world and the demand for its secularization and modernization. These two different political constellations eventually found a common political platform in 1975 with the creation of Khamsin. Finally, the chapter illustrates how Khamsin provided a political platform that opposed the rise of religious fundamentalism and Islamization in the Middle East. Socialist internationalism seemed to point to a common future beyond national and religious partisanship.