104,211 research outputs found
Dense Graphs Have Rigid Parts
No full textWhile the problem of determining whether an embedding of a graph G in ℝ² is infinitesimally rigid is well understood, specifying whether a given embedding of G is rigid or not is still a hard task that usually requires ad hoc arguments. In this paper, we show that every embedding (not necessarily generic) of a dense enough graph (concretely, a graph with at least C₀n^{3/2}(log n)^β edges, for some absolute constants C₀>0 and β), which satisfies some very mild general position requirements (no three vertices of G are embedded to a common line), must have a subframework of size at least three which is rigid. For the proof we use a connection, established in Raz [Discrete Comput. Geom., 2017], between the notion of graph rigidity and configurations of lines in ℝ³. This connection allows us to use properties of line configurations established in Guth and Katz [Annals Math., 2015]. In fact, our proof requires an extended version of Guth and Katz result; the extension we need is proved by János Kollár in an Appendix to our paper.
We do not know whether our assumption on the number of edges being Ω(n^{3/2}log n) is tight, and we provide a construction that shows that requiring Ω(n log n) edges is necessary
Wedrówki Ahaswera : Poemat Józefa Chrzécijana barona Zedlitza, po raz pierwszy wydany polskim i zaopatrzony wstepnem slowem / przez G. Kohna ...
No full textWEDRÓWKI AHASWERA : POEMAT JÓZEFA CHRZÉCIJANA BARONA ZEDLITZA, PO RAZ PIERWSZY WYDANY POLSKIM I ZAOPATRZONY WSTEPNEM SLOWEM / PRZEZ G. KOHNA ...
Wedrówki Ahaswera : Poemat Józefa Chrzécijana barona Zedlitza, po raz pierwszy wydany polskim i zaopatrzony wstepnem slowem / przez G. Kohna ... (1)
Cover (1)
Titelseite (5)
Przedmowa (7)
Kornel Ajejski (17)
I. (19)
II. (29)
III. (44
Configurations of Lines in 3-Space and Rigidity of Planar Structures
No full textLet L be a sequence (l_1,l_2,...,l_n) of n lines in C^3. We define the intersection graph G_L=([n],E) of L, where [n]:={1,..., n}, and with {i,j} in E if and only if i\neq j and the corresponding lines l_i and l_j intersect, or are parallel (or coincide). For a graph G=([n],E), we say that a sequence L is a realization of G if G subset G_L. One of the main results of this paper is to provide a combinatorial characterization of graphs G=([n],E) that have the following property: For every generic realization L of G, that consists of n pairwise distinct lines, we have G_L=K_n, in which case the lines of L are either all concurrent or all coplanar.
The general statements that we obtain about lines, apart from their independent interest, turns out to be closely related to the notion of graph rigidity. The connection is established due to the so-called Elekes-Sharir framework, which allows us to transform the problem into an incidence problem involving lines in three dimensions. By exploiting the geometry of contacts between lines in 3D, we can obtain alternative, simpler, and more precise characterizations of the rigidity of graphs
Polynomial Bounds on Parallel Repetition for All 3-Player Games with Binary Inputs
No full textWe prove that for every 3-player (3-prover) game G with value less than one, whose query distribution has the support S = {(1,0,0), (0,1,0), (0,0,1)} of Hamming weight one vectors, the value of the n-fold parallel repetition G^{⊗n} decays polynomially fast to zero; that is, there is a constant c = c(G) > 0 such that the value of the game G^{⊗n} is at most n^{-c}.
Following the recent work of Girish, Holmgren, Mittal, Raz and Zhan (STOC 2022), our result is the missing piece that implies a similar bound for a much more general class of multiplayer games: For every 3-player game G over binary questions and arbitrary answer lengths, with value less than 1, there is a constant c = c(G) > 0 such that the value of the game G^{⊗n} is at most n^{-c}.
Our proof technique is new and requires many new ideas. For example, we make use of the Level-k inequalities from Boolean Fourier Analysis, which, to the best of our knowledge, have not been explored in this context prior to our work
A brief overview of the history of the Jews in Italy: according to Dubnov
No full textPrvi politički doticaji Judeje i Rima sežu u 2. vijek prije Krista, kad je (161-160 godine) Juda Makabi sklopio s Rimom savez za zaštitu protiv Sirije po kome su obje strane bile obvezane da se uzajamno pomognu u slučaju rata u Orijentu. Kako se odnos Rima prema Jeruzalimu doskora stao razvijati u pravcu osvajanja zemlje judejske i njezina razorenja, dovoljno je poznato. U ovoj knjizi se daje prikaz o počecima naseljavanja Židova u Italiji. U isto vrijeme kad i u Grčkoj, u 2. vijeku pr. Hr., pojavljuju se židovske kolonije u Italiji. Rimski istoričar Valerius Maximus izvještava, da su za konzulata Popilija Laenasa i Kalpurnija (139 g. pr. Hr.) vlasti izagnale Židove „koji su nastojali da naude rimskim običajima kultom Jupitra Sabacija“ (očito je istoričar zamijenio kult šabata s ovim frigijskim božanstvom). Ali se prvi puta iza 63. godine pr. Hr. pojavljuje znatna židovska kolonija u Rimu. Bili su to zarobljenici koje je poslije osvojenja Jeruzalima Pompej poveo u Rim, gdje su prodati kao roblje. Mnogi od njih bili su doskora ili oslobođeni ili od svojih rođaka otkupljeni, pa su ostali i dalje u Rimu, gdje su, udruživši se u općinu, živjeli u zasebnoj gradskoj četvrti na obali Tibera. Poznat je iz onoga doba proces protiv rimskog prokonzula u Aziji Valerija Flaka zbog zloupotreba u zvaničnoj dužnosti i utaja, među ostalim i utaje velike svote koju su maloazijski Židovi bili skupili za jeruzalimski hram. Branio je Flaka Cicero! U njegovom govoru došao je do izražaja sav prezir pobjedničkog naroda prema pobijeđenome. Sirci i Židovi njemu su bili „narodi rođeni za robovanje“. Judaizam, kao vjera, bila je njemu „barbara superstitio“. Protivno te netrpeljivosti tog konzervativnog državnika Cicera, Julije Cezar, njegov savremenik, redovno je štitio prava židovske općine u Rimu, upravo onako, kako je to činio u Maloj Aziji, pa je ona uzela živog učešća u javnom životu iza njegove nasilne smrti. Sueton izvještava da su Židovi noćima držali stražu kraj Cezarova pepela i gorko oplakivali njegovu smrt. Pod Augustom još se uvećala židovska kolonija u Rimu. Po izvještaju Josefa Flavija 8.000 rimskih Židova potpomoglo je traženje izaslanstva jeruzalimskih građana da se Judeja preobrati u slobodnu narodnu državu. Ostavši vjerni svojoj religiji, oni su provodili i vjersku propagandu, sad u vidu starožidovske predaje, sad u vidu prahrišćanstva koje se u ono doba teško dalo razlikovati od judaizma, da bi, kasnije, židovsko-helenistički sinkretizam napravio mjesta hrišćansko-helenističkome. Kad su se ovi vjerski nazori stali u Rimu i u ostaloj Italiji sve više širiti, car Tiberije (14-37), taj okrutni čovjekomrzac, stao je da progoni Židove, ali je, po smrti svoga savjetnika Sejana, naredio vlastima da ne ometaju Židove u vršenju njihovih obreda.The first political contacts between Judea and Rome date back to the 2nd century BCE, when Judas Maccabeus (161-160 BCE) concluded an alliance with Rome against Syria. Rome’s attitude toward Jerusalem later became expansionist. In the 2nd century BCE, Jews began settling in Italy, at the same time as in Greece. The Roman historian Valerius Maximus reports the expulsion of Jews in 139 BCE for the “cult of Jupiter Sabazius,” a probable misinterpretation of the Sabbath. A significant Jewish community appeared in Rome after 63 BCE, when Pompey brought captives from Jerusalem. Many were freed or ransomed and settled in a district along the Tiber. Despite the contempt of conservative Roman politicians like Cicero, Jews participated in public life, while Julius Caesar regularly protected their rights. Under Augustus, the community grew; 8,000 Roman Jews supported a delegation seeking Judea’s freedom. They maintained their religion and spread religious ideas, later contributing to Judeo-Hellenistic and early Christian syncretism. Emperor Tiberius attempted persecutions, but after the death of his advisor Sejanus, he ordered that Jews be allowed to practice their rites freely.Biblioteka Židov ; 10.Na zadnjoj korici knjige dat je spisak „Redovitih“ i „Ranijih“ izdanja biblioteke „Židov“ Zagreb, uz sledeću napomenu: Ove se knjige mogu naručiti kod Saveza cionista Jugoslavije, Zagreb, Dolac 9. Pošt. pret. 383
"Why should I be moral?" : a critical assessment of three contemporary attempts to give an extra-moral justification of moral conduct
No full textIn this dissertation I consider three distinct attempts to answer the normative question “Why should I be moral?”, all of which assume that a successful answer must be capable of arguing someone who is currently not motivated by moral considerations at all into becoming moral. I outline an argument against the possibility of doing so which relies on the distinction between agent-relativity and agent-neutrality, and which states that since morality essentially involves agent-neutrality and since failure to recognize the reason-giving force of agent-neutral considerations is not necessarily irrational, one cannot be argued into being moral. I then show how the approaches of Christine Korsgaard, as encountered in her "The Sources of Normativity", Joseph Raz, as he puts it forth in “The Amoralist”, and lastly, David Brink as he puts it forth in “Self-Love and Altruism”, each in their different ways, fail in their attempts to argue someone into becoming moral
Recommended from our members
Time-Space Tradeoffs for Distinguishing Distributions and Applications to Security of Goldreich’s PRG
No full textIn this work, we establish lower-bounds against memory bounded algorithms for distinguishing between natural pairs of related distributions from samples that arrive in a streaming setting.
Our first result applies to the problem of distinguishing the uniform distribution on {0,1}ⁿ from uniform distribution on some unknown linear subspace of {0,1}ⁿ. As a specific corollary, we show that any algorithm that distinguishes between uniform distribution on {0,1}ⁿ and uniform distribution on an n/2-dimensional linear subspace of {0,1}ⁿ with non-negligible advantage needs 2^Ω(n) samples or Ω(n²) memory (tight up to constants in the exponent).
Our second result applies to distinguishing outputs of Goldreich’s local pseudorandom generator from the uniform distribution on the output domain. Specifically, Goldreich’s pseudorandom generator G fixes a predicate P:{0,1}^k → {0,1} and a collection of subsets S₁, S₂, …, S_m ⊆ [n] of size k. For any seed x ∈ {0,1}ⁿ, it outputs P(x_S₁), P(x_S₂), …, P(x_{S_m}) where x_{S_i} is the projection of x to the coordinates in S_i. We prove that whenever P is t-resilient (all non-zero Fourier coefficients of (-1)^P are of degree t or higher), then no algorithm, with < n^ε memory, can distinguish the output of G from the uniform distribution on {0,1}^m with a large inverse polynomial advantage, for stretch m ≤ (n/t) ^{(1-ε)/36 ⋅ t} (barring some restrictions on k). The lower bound holds in the streaming model where at each time step i, S_i ⊆ [n] is a randomly chosen (ordered) subset of size k and the distinguisher sees either P(x_{S_i}) or a uniformly random bit along with S_i.
An important implication of our second result is the security of Goldreich’s generator with super linear stretch (in the streaming model), against memory-bounded adversaries, whenever the predicate P satisfies the necessary condition of t-resiliency identified in various prior works.
Our proof builds on the recently developed machinery for proving time-space trade-offs (Raz 2016 and follow-ups). Our key technical contribution is to adapt this machinery to work for distinguishing problems in contrast to prior works on similar results for search/learning problems
Imaging techniques in ALS
No full textAmyotrophic Lateral Sclerosis (ALS) is a progressive neurodegenerative disease characterized by degeneration of both upper and lower motor neuron located in the spinal cord and brainstem. Diagnosis of ALS is predominantly clinical, nevertheless, electromyography and Magnetic Resonance Imaging (MRI) may provide support. Several advanced MRI techniques have been proven useful for ALS diagnosis and, indeed, the combination of different MRI techniques demonstrated an improvement in sensitivity and specificity as far as 90%. This review focus on the imaging techniques currently used in the diagnosis and management of ALS with brief considerations on future applications
Visual Feedback Postural Control Re-education
No full textMaintaining postural stability is a complex process [1] involving the coordinated actions of biomechanical, sensory, motor, and central nervous system components. A relatively simple biomechanical definition for postural stability can be formulated in terms of the position of the body center of gravity relative to the base of support. The body movements used to maintain postural stability, however, are complex because of the number of joint systems and muscles involved. The center of gravity (CoG) is the point at which the whole weight of a body may be considered to act. In humans who are standing quietly and vertically erect, the CoG is located at the level of the hips and slightly forward of the ankle joints. CoG height is 0.5527 of total height. CoG and center of mass (CoM) are equivalent points in space when the gravitational field is uniform and gravity is the only force under consideration
- …
