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1. Search for a scalar partner of the top quark in the all-hadronic $$t{\bar{t}}$$ plus missing transverse momentum final state at $$\sqrt{s}=13$$ TeV with the ATLAS detector

   https://doi.org/10.1140/epjc/s10052-020-8102-8  

   Aad, G.; Abbott, B.; Abbott, D. C.; Abud, A. Abed; Abeling, K.; Abhayasinghe, D. K.; Abidi, S. H.; AbouZeid, O. S.; Abraham, N. L.; Abramowicz, H.; et al (August 2020, The European Physical Journal C)

   null (Ed.)

   Abstract A search for direct pair production of scalar partners of the top quark (top squarks or scalar third-generation up-type leptoquarks) in the all-hadronic $$t{\bar{t}}$$ t t ¯ plus missing transverse momentum final state is presented. The analysis of 139  $$\hbox {fb}^{-1}$$ fb - 1 of $${\sqrt{s}=13}$$ s = 13  TeV proton–proton collision data collected using the ATLAS detector at the LHC yields no significant excess over the Standard Model background expectation. To interpret the results, a supersymmetric model is used where the top squark decays via $${\tilde{t}} \rightarrow t^{(*)} {\tilde{\chi }}^0_1$$ t ~ → t ( ∗ ) χ ~ 1 0 , with $$t^{(*)}$$ t ( ∗ ) denoting an on-shell (off-shell) top quark and $${\tilde{\chi }}^0_1$$ χ ~ 1 0 the lightest neutralino. Three specific event selections are optimised for the following scenarios. In the scenario where $$m_{{\tilde{t}}}> m_t+m_{{\tilde{\chi }}^0_1}$$ m t ~ > m t + m χ ~ 1 0 , top squark masses are excluded in the range 400–1250 GeV for $${\tilde{\chi }}^0_1$$ χ ~ 1 0 masses below 200 GeV at 95% confidence level. In the situation where $$m_{{\tilde{t}}}\sim m_t+m_{{\tilde{\chi }}^0_1}$$ m t ~ ∼ m t + m χ ~ 1 0 , top squark masses in the range 300–630 GeV are excluded, while in the case where $$m_{{\tilde{t}}}< m_W+m_b+m_{{\tilde{\chi }}^0_1}$$ m t ~ < m W + m b + m χ ~ 1 0 (with $$m_{{\tilde{t}}}-m_{{\tilde{\chi }}^0_1}\ge 5$$ m t ~ - m χ ~ 1 0 ≥ 5  GeV), considered for the first time in an ATLAS all-hadronic search, top squark masses in the range 300–660 GeV are excluded. Limits are also set for scalar third-generation up-type leptoquarks, excluding leptoquarks with masses below 1240 GeV when considering only leptoquark decays into a top quark and a neutrino. 

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2. Joint Poisson distribution of prime factors in sets

   https://doi.org/10.1017/S0305004121000499  

   FORD, KEVIN (July 2022, Mathematical Proceedings of the Cambridge Philosophical Society)

   Abstarct Given disjoint subsets T 1 , …, T m of “not too large” primes up to x , we establish that for a random integer n drawn from [1, x ], the m -dimensional vector enumerating the number of prime factors of n from T 1 , …, T m converges to a vector of m independent Poisson random variables. We give a specific rate of convergence using the Kubilius model of prime factors. We also show a universal upper bound of Poisson type when T 1 , …, T m are unrestricted, and apply this to the distribution of the number of prime factors from a set T conditional on n having k total prime factors. 

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3. L oo p D e l t a : E m b e dd i n g L o c a li t y - a w a r e O pp o r t un i s t i c D e l t a C o m p r e ss i o n i n I n li n e D e dup li c a t i o n f o r Hi g h l y E ffic i e n t D a t a R e du c t i o n

   Zhang, Yucheng; Jiang, Hong; Feng, Dan; Jiang Nan; Qui, Taorong; Huang, Wei (July 2023, USENIX annual technical conference)

   A s a c om pl e men t t o da ta d edupli cat ion , de lta c om p ress i on fu r- t he r r edu c es t h e dat a vo l u m e by c o m pr e ssi n g n o n - dup li c a t e d ata chunk s r e l a t iv e to t h e i r s i m il a r chunk s (bas e chunk s). H ow ever, ex is t i n g p o s t - d e dup li c a t i o n d e l t a c o m pr e ssi o n a p- p ro a ches fo r bac kup s t or ag e e i t h e r su ffe r f ro m t h e l ow s i m - il a r i t y b e twee n m any de te c ted c hun ks o r m i ss so me po t e n - t i a l s i m il a r c hunks , o r su ffer f r om l ow (ba ckup and r es t ore ) th r oug hpu t du e t o extr a I/ Os f or r e a d i n g b a se c hun ks o r a dd a dd i t i on a l s e r v i c e - d i s r up t ive op e r a t i on s to b a ck up s ys t em s. I n t h i s pa p e r, w e pr opo se L oop D e l t a t o a dd ress the above - m e n t i on e d prob l e m s by an e nha nced em b e ddi n g d e l t a c o m p - r e ss i on sc heme i n d e dup li c a t i on i n a non - i n t ru s ive way. T h e e nha nce d d elt a c o mpr ess ion s che m e co m b in e s f our key t e c h - ni qu e s : (1) du a l - l o c a li t y - b a s e d s i m il a r i t y t r a c k i n g to d e t ect po t e n t i a l si m il a r chun k s b y e x p l o i t i n g both l o g i c a l and ph y - s i c a l l o c a li t y, ( 2 ) l o c a li t y - a wa r e pr e f e t c h i n g to pr efe tc h ba se c hun ks to a vo i d ex t ra I/ Os fo r r e a d i n g ba s e chun ks on t h e w r i t e p at h , (3) c a che -aware fil t e r to avo i d ext r a I/Os f or b a se c hunk s on t he read p at h, a nd (4) i nver sed de l ta co mpressi on t o perf orm de lt a co mpress i o n fo r d at a chunk s t hat a re o th e r wi se f o r b i dd e n to s er ve as ba se c hunk s by r ew r i t i n g t e c hn i qu e s d e s i g n e d t o i m p r ove r es t o re pe rf o rma nc e. E x p e r i m e n t a l re su lts indi ca te t hat L oop D e l t a i ncr ea se s t he c o m pr e ss i o n r a t i o by 1 .2410 .97 t i m e s on t op of d e dup li c a - t i on , wi t hou t no t a b l y a ffe c t i n g th e ba ck up th rou ghpu t, a nd i t i m p r ove s t he res to re p er fo r m an ce b y 1.23.57 t i m e 

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4. 2D Ising Field Theory in a magnetic field: the Yang-Lee singularity

   https://doi.org/10.1007/JHEP08(2022)057  

   Xu, Hao-Lan; Zamolodchikov, Alexander (August 2022, Journal of High Energy Physics)

   A bstract We study Ising Field Theory (the scaling limit of Ising model near the Curie critical point) in pure imaginary external magnetic field. We put particular emphasis on the detailed structure of the Yang-Lee edge singularity. While the leading singular behavior is controlled by the Yang-Lee fixed point (= minimal CFT $$ \mathcal{M} $$ M 2 / 5 ), the fine structure of the subleading singular terms is determined by the effective action which involves a tower of irrelevant operators. We use numerical data obtained through the “Truncated Free Fermion Space Approach” to estimate the couplings associated with two least irrelevant operators. One is the operator $$ T\overline{T} $$ T T ¯ , and we use the universal properties of the $$ T\overline{T} $$ T T ¯ deformation to fix the contributions of higher orders in the corresponding coupling parameter α . Another irrelevant operator we deal with is the descendant L_ 4 $$ \overline{L} $$ L ¯ _ 4 ϕ of the relevant primary ϕ in $$ \mathcal{M} $$ M 2 / 5 . The significance of this operator is that it is the lowest dimension operator which breaks integrability of the effective theory. We also establish analytic properties of the particle mass M (= inverse correlation length) as the function of complex magnetic field. 

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5. Duality for Optimal Couplings in Free Probability

   https://doi.org/10.1007/s00220-022-04480-0  

   Gangbo, Wilfrid; Jekel, David; Nam, Kyeongsik; Shlyakhtenko, Dimitri (December 2022, Communications in Mathematical Physics)

   Abstract We study the free probabilistic analog of optimal couplings for the quadratic cost, where classical probability spaces are replaced by tracial von Neumann algebras, and probability measures on $${\mathbb {R}}^m$$ R m are replaced by non-commutative laws of m -tuples. We prove an analog of the Monge–Kantorovich duality which characterizes optimal couplings of non-commutative laws with respect to Biane and Voiculescu’s non-commutative $$L^2$$ L 2 -Wasserstein distance using a new type of convex functions. As a consequence, we show that if ( X ,  Y ) is a pair of optimally coupled m -tuples of non-commutative random variables in a tracial $$\mathrm {W}^*$$ W ∗ -algebra $$\mathcal {A}$$ A , then $$\mathrm {W}^*((1 - t)X + tY) = \mathrm {W}^*(X,Y)$$ W ∗ ( ( 1 - t ) X + t Y ) = W ∗ ( X , Y ) for all $$t \in (0,1)$$ t ∈ ( 0 , 1 ) . Finally, we illustrate the subtleties of non-commutative optimal couplings through connections with results in quantum information theory and operator algebras. For instance, two non-commutative laws that can be realized in finite-dimensional algebras may still require an infinite-dimensional algebra to optimally couple. Moreover, the space of non-commutative laws of m -tuples is not separable with respect to the Wasserstein distance for $$m > 1$$ m > 1 . 

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