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Opisali smo naravno vibracijsko okolje škržatkov iz rodu Aphrodes, ki živijo v travniškem habitatu. Vibracijska krajina na travniku se je pokazala kot nizko-frekvenčno okolje, v katerem šibek veter povzroča stalen abiotski vibracijski šum. Vibracijski dogodki, ki so posledica aktivnosti biološke komponente vibracijske krajine, iz tega abiotskega šuma izstopajo predvsem po frekvenci. Vibracijska krajina, ki smo jo registrirali na travniku, se je tekom sezone od maja do oktobra razlikovala tako po abundanci (oz. časovni zasedenosti) kot po sestavi (oz. tipih vibracijskih signalov, ki smo jih registrirali). Pestrost signalov v določenem dnevu ni bila povezana z abundanco. Tekom sezone smo registrirali 56 različnih tipov signalov, vendar akumulacijske krivulje kažejo, da je bila diverziteta signalov po vsej verjetnosti večja, kot smo jo lahko zaznali z našim časovno omejenim terenskim vzorčenjem. Aktivnost vibracijske združbe je bila najvišja v sredini dneva in popoldne ter najnižja ponoči. Dnevno-nočne razlike v aktivnosti vibracijske združbe, so povezane s temperaturo okolja. S stališča sprejemnika, je travniška vibracijska krajina pestra, tako zaradi velikega števila različnih signalov kot tudi zaradi njihove fluktuacije in s tem hitrega speminjanja sestave vibracijske krajine. Prekrivanje vibracijskih signalov je bilo značilno manjše, kot če bi se vibracijski signali v vibracijski krajini pojavljali naključno. Člani raziskovane travniške vibracijske združbe se medsebojnemu motenju izogibajo z razdelitvijo vibracijskega komunikacijskega prostora v času tako, da se izmenjujejo v oddajanju signalov. We described the natural vibrational environment (i.e. vibroscape) of Aphrodes leafhoppers living in a meadow habitat. Meadow vibroscape was a low-frequency environment where wind of low velocity induced in plants nearly constant abiotic vibrational noise. Vibrational events originating from biological sources stood out from abiotic noise primarily in frequency domain. The vibroscape composition was changing throughout the season from May till October in the signal richness (number of different types of vibrationals) as well as in signal abundance (cummulative duration of vibrational signals). Time occupancy of vibrational communication channel was not correlated with signal richness registred on that day. Throughout the season we registered 56 different types of vibrational signal however, signal accumulation curves suggest that signal diversity was most likely higher than revealed by our time-limited field recordings. The signalling activity of vibrational community was highest in the middle of the day and in the afternoon and lowest during the night. Such dial pattern of vibrational activity is regulated by temperature. From the perspective of a receiver, the meadow vibroscape is a complex and dynamic environment, rich in species-specific vibrational signals and characterized by their high turnover. The overlap of vibrational signals was significantly lower that it would by chance. The members of investigated meadow vibrational community were avoiding interference primarily by partitioning vibrational space on fine temporal scale by avoiding signalling at times with hight background biotic noise.

We give upper and lower bounds on the power of subsystems of the Ideal Proof System (IPS), the algebraic proof system recently proposed by Grochow and Pitassi (J. ACM, 2018), where the circuits comprising the proof come from various restricted algebraic circuit classes. This mimics an established research direction in the Boolean setting for subsystems of Extended Frege proofs, where proof-lines are circuits from restricted Boolean circuit classes. Except one, all of the subsystems considered in this paper can simulate the well-studied Nullstellensatz proof system, and prior to this work there were no known lower bounds when measuring proof size by the algebraic complexity of the polynomials (except with respect to degree, or to sparsity). We give two general methods of converting certain algebraic circuit lower bounds into proof complexity ones. However, we need to strengthen existing lower bounds to hold for either the functional model or for multiplicities (see below). Our techniques are reminiscent of existing methods for converting Boolean circuit lower bounds into related proof complexity results, such as feasible interpolation. We obtain the relevant types of lower bounds for a variety of classes (sparse polynomials, depth-3 powering formulas, read-once oblivious algebraic branching programs, and multilinear formulas), and infer the relevant proof complexity results. We complement our lower bounds by giving short refutations of the previously studied subset-sum axiom using IPS subsystems, allowing us to conclude strict separations between some of these subsystems. Our first method is a functional lower bound, a notion due to Grigoriev and Razborov (Appl. Algebra Eng. Commun. Comput., 2000), which says that not only does a polynomial f require large algebraic circuits, but that any polynomial g agreeing with f on the Boolean cube also requires large algebraic circuits. For our classes of interest, we develop functional lower bounds where g(x¯¯¯) equals 1/p(x¯¯¯) where p is a constant-degree polynomial, which in turn yield corresponding IPS lower bounds for proving that p is nonzero over the Boolean cube. In particular, we show superpolynomial lower bounds for refuting variants of the subset-sum axiom in various IPS subsystems. Our second method is to give lower bounds for multiples, that is, to give explicit polynomials whose all (nonzero) multiples require large algebraic circuit complexity. By extending known techniques, we are able to obtain such lower bounds for our classes of interest, which we then use to derive corresponding IPS lower bounds. Such lower bounds for multiples are of independent interest, as they have tight connections with the algebraic hardness versus randomness paradigm.

Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their orthogonal complements in the finite-dimensional complex vector space. We shall establish a variety of closed-form formulas for representing the direct sum decompositions of them-dimensional complex column vector space 𝔺mwith respect to a pair of given linear subspaces 𝒨 and 𝒩 and their operations, and use them to derive a huge amount of decomposition identities for matrix expressions composed by a pair of orthogonal projectors onto the linear subspaces. As applications, we give matrix representation for the orthogonal projectors onto the intersections of a pair of linear subspaces using various matrix decomposition identities and Moore–Penrose inverses; necessary and su˚cient conditions for two linear subspaces to be in generic position; characterization of the commutativity of a pair of orthogonal projectors; necessary and su˚cient conditions for equalities and inequalities for a pair of subspaces to hold; equalities and inequalities for norms of a pair of orthogonal projectors and their operations; as well as a collection of characterizations of EP-matrix.

In a Hilbert space $${{\mathcal {H}}}$$ , we study the convergence properties of a class of relaxed inertial forward–backward algorithms. They aim to solve structured monotone inclusions of the form $$Ax + Bx \ni 0$$ where $$A:{{\mathcal {H}}}\rightarrow 2^{{\mathcal {H}}}$$ is a maximally monotone operator and $$B:{{\mathcal {H}}}\rightarrow {{\mathcal {H}}}$$ is a cocoercive operator. We extend to this class of problems the acceleration techniques initially introduced by Nesterov, then developed by Beck and Teboulle in the case of structured convex minimization (FISTA). As an important element of our approach, we develop an inertial and parametric version of the Krasnoselskii–Mann theorem, where joint adjustment of the inertia and relaxation parameters plays a central role. This study comes as a natural extension of the techniques introduced by the authors for the study of relaxed inertial proximal algorithms. An illustration is given to the inertial Nash equilibration of a game combining non-cooperative and cooperative aspects.

Sintetizatori frekvencija se koriste kada je potrebno održavati točno određenu frekvenciju izlaznog signala. Stabilnost sintetizatora osigurava se sklopom za sinkronizaciju faze (Phase- Locking Loop, PLL). U povratnoj vezi PLL-a nalazi se necjelobrojno djelilo frekvencije kojime se odabire točan kanal i smanjuje frekvencija kako bi ostali sklopovi u sintetizatoru mogli raditi na manjim brzinama. Zbog rada na visokim frekvencijama, u projektiranju djelila potrebno je kombinirati CML logički stil (strujom upravljane krugove) i standardnu logiku. U ovome radu se analizira i projektira necjelobrojno djelilo frekvencije za komunikacije na 2 GHz s tehnikama oblikovanja šuma pomoću sigma-delta modulatora. A frequency synthesizer is used to maintain a specific frequency of a signal. A synthesizer is made of a Phase-Locking Loop which ensures the stability of the frequency at its exit. The loop has a negative feedback with a frequency divider which is used for selecting the channels and reducing the frequency so the rest of the loop can work at lower speed. Because of its high operating frequency, the divider design combines CML logic style (Current-Mode Logic) and standard logic at lower frequencies. In this research you can find a complete analyses and design procedure of the fractional frequency divider, including noise shaping using sigma-delta modulator.

Syftet med denna kunskapsöversikt är att redogöra för vilka arbetsformer som presenteras i forskning som gynnsamma för elever i matematiksvårigheter i årskurserna F-3. För att kunna besvara detta krävs inledningsvis en redogörelse för vilka olika former av matematiksvårigheter som skrivs fram i forskning som förekommande i årskurserna F-3. Syftet har således delats in i två frågeställningar: Vilka olika former av matematiksvårigheter presenteras i forskning, och vilka förklaringar redogörs för varför elever hamnar i matematiksvårigheter? Samt vilka arbetsformer skrivs fram i forskning som gynnsamma för elever i matematiksvårigheter? Metoden som användes för att finna adekvat forskning var i största utsträckning en datorbaserad litteratursökning, men även manuella sekundärsökningar tillämpades som metod. För att finna relevant forskning att belysa i kunskapsöversikten söktes med hjälp av adekvata nyckelord flertalet forskningsrapporter, doktorsavhandlingar och artiklar upp via databaserna SwePub och ERC. Dessa granskades och säkerställdes att de var av vetenskaplig karaktär. Vidare undersöktes källornas referenslistor i den utvalda forskningen, vilket utmynnade i ett antal sekundärkällor av relevans för kunskapsöversiktens frågeställningar. Som stöd för våra val av källor har Backman (2016) och Östlundh (2017) varit till stor hjälp. Resultatet av den litteratursökning som gjorts mynnade ut i relevant forskning som användes och gav svar på kunskapsöversiktens frågeställningar. Kunskapsöversiktens resultat är tematiskt och uppdelat i två huvudfrågor vilka kom att sätta grunden för rådande underrubriker. Resultatet presenterar specifika- och generella matematiksvårigheter samt särskilda utbildningsbehov i matematik (SUM). Resultatet redogör för kognitiva, medicinska, pedagogiska, känslomässiga och miljömässiga förklaringar och faktorer som beskriver varför elever hamnar i matematiksvårigheter. Det framgår även i resultatet flertalet gynnsamma arbetssätt för elever i matematiksvårigheter. I resultatet redovisas: Inkludering, intensivundervisning, kooperativt arbete, formativ bedömning, högläsning, samt läsplatta. Slutsatsen av resultatet påvisar att det finns flertalet lämpliga metoder för att arbeta med elever i matematiksvårigheter. I slutsatsen redogörs även för eventuella konsekvenser av de olika arbetsformerna. Nyckelord: Dyskalkyli, generella matematiksvårigheter, inkludering, kooperativt arbete, matematiksvårigheter, specifika matematiksvårigheter, SUM, särskilt stöd

U ovom radu dizajnirani su naponski kontrolirani oscilatori sa strujnim zrcalom za napajanje. Specifikacije koje su postvljene su centralna frekvencija 2.4 GHz i raspon ugađanja frekvencije +/- 10% od centralne frekvencije. Projektirane su dvije verzije oscilatora s unakrsno spojenim NMOS parom te 2 unakrsno spojena NMOS i PMOS para. Napravljena je optimizacija s obzirom na amplitudu oscilacija, disipaciju snage, frekvencijski raspon ugađanja i fazni šum. In this paper, voltage controlled oscillators with a current mirror power supply are designed. The specifications are: the 2.4 GHz center frequency and the frequency tuning range +/- 10% of the center frequency. Two versions of the oscillator with cross-coupled NMOS pair and 2 cross-coupled NMOS and PMOS pairs have been designed. Optimization was made with respect to oscillation amplitude, power dissipation, frequency tuning range, and phase noise.

Iako najčešće zahvaća gornji respiratorni sustav sa simptomima vrućice, kašlja i umora, novi virus SARS-COV-2 može dovesti do pneumonije i težih komplikacija poput multiorganskog zatajenja. Kako pandemija pogađa sve veći broj osoba, pojavljuju se sve više simptomi koji nisu usko povezani s gornjim dišnjim sustavom. Javljaju se gastrointestinalni simptomi, neurološki i kardiološki simptomi, kožne promjene, te simptomi unutrašnjeg i srednjeg uha, poput gubitka sluha, tinitusa, otalgije i vrtoglavica. Moguća patogeneza virusno-induciranog gubitka sluha je u izravnom oštećenju stuktura unutrašnjeg uha ili u imunološki posredovanom odgovoru. Cilj rada je bio analizirati i prikazati bolesnike s audiovestibularnim simptomima kao kliničkim manifestacijama SARS-COV-2 infekcije. Analizirirali smo 25 bolesnika u dobi između 33 i 70 godina koji su se javili u audiološku ambulantu u vremenu od 01. prosinca 2020. godine do 06. veljače 2021. godine sa simptomima gubitka sluha, tinitusom i vrtoglavicom. Rezultati studije pokazuju da je došlo do akutnog jednostranog gubitka sluha u 2 bolesnika, a do akutnog obostranog u jednog bolesnika tijekom SARS-COV-2 infekcije. U jednog bolesnika došlo je do potpunog oporavka sluha nakon kortikosteroidne terapije, a u dvojice do djelomičnog oporavka. Do gubitka sluha samo u visokim frekvencijama na 4000 i 6000 Hz obostrano, došlo je u 13 bolesnika. Radi se ujedno o najkarakterističnijem i najčešćem nalazu sluha. Također vidimo da je došlo do egzacerbacije tinitusa u 4 bolesnika, a do novonastalnog tinitusa u 11 bolesnika. Vrtoglavica se javila u 3 bolesnika i radi se o novonastalim vrtoglavicama. Iako smo otkrili vezu između koronavirusa i gubitka sluha, tinitisa i vrtoglavice, još uvijek ne znamo prevalenciju audioloških manifestacija bolesti, jer je i dalje fokus na težim i životno ugrožavajućim stanjima, pa se smetnje sluha i ravnoteže često zanemaruju ili se čeka na mogući spontani oporavak i time gubi dragocjeno vrijeme za liječenje i mogući brži oporavak.

Este documento plantea el proceso y la aplicación de una investigación que diseñó una estrategia didáctica mediada por las Tecnologías de la Información y las Comunicación (TIC) para promover el aprendizaje de la operación adición a un niño con Síndrome Down. Esta buscó determinar el desarrollo de la noción suma a través de una prueba diagnóstica para diseñar y aplicar actividades que fortalecerían la operación adición. Finalmente, a través de la observación y los resultados propios de la estrategia se evaluó su efectividad, permitiendo de esta manera realizar modificaciones finales a la estrategia. Guiados por el paradigma cualitativo y teniendo como diseño metodológico el estudio de caso, se buscó mejorar las prácticas educativas. Mediante la estrategia didáctica se orientaron los procesos de enseñanza y aprendizaje en la dimensión matemática, más específicamente la operación adición, en un niño con síndrome Down. La estrategia destaca la importancia de generar inclusión en el sistema educativo a niños Down para favorecer el aprendizaje en matemáticas y en la operación adición, siendo esta propuesta una forma de intervenir tanto en el trastorno como en los procesos de aprendizaje. A través de la estrategia se desarrolló el aprendizaje de una noción matemática adecuada teniendo en cuenta que el trastorno hace hincapié en procesos cognitivos y de aprendizaje, de modo que, el trastorno es una variable que se relaciona en el diseño y desarrollo de las actividades. Esto facilitó la atención en las clases virtuales generando un impacto significativo en el niño Down, afrontando la pandemia actual y sintiéndose motivado por el contexto educativo virtual. Introducción 15 Capítulo I. Planteamiento del Problema 16 Descripción del Problema 16 Justificación 19 Supuestos de investigación 22 Objetivos 23 Objetivo General. 23 Objetivos Específicos. 23 Capítulo II. Marco de Teórico y Referencial 24 La Inclusión 25 Aproximación sobre la educación inclusiva. 29 El ambiente de aprendizaje del aula inclusiva 31 Estrategias de Enseñanza de las Matemáticas 34 Uso De La Tecnología 36 Estado del arte 38 Antecedentes 38 Antecedentes Internacionales 38 Antecedentes Nacionales 42 Antecedentes Locales 44 Marco Conceptual 46 9 Síndrome de Down (Sd) 46 Definición 46 Características Psicológicas y del Aprendizaje en Personas con SD 49 Marco Normativo 51 Capítulo III. Metodología 54 Método de estudio 54 Fases método de investigación 55 Fases del proceso 56 Fase de reflexión 56 Fase de observación y diagnóstico. 57 Fase de planificación. 61 Fase de ejecución. 63 Población, Participantes y Selección de la Muestra 64 Instrumentos de recolección de datos 64 Prueba diagnóstica 65 Observación – Diarios Pedagógicos 65 Rejillas de relación y análisis 67 Consentimientos Informados 67 Herramientas Mediada por las TIC 68 Procedimiento en la aplicación de instrumentos 69 Análisis de datos 69 Diseño de la estrategia 69 Categorías 72 Planificación del Proceso de Enseñanza 72 Estrategias Didácticas mediada por las TIC 73 Recursos 74 Perfil del Maestro 75 Desarrollo y aplicación de la estrategia 76 Categorías 78 Funcionamientos Cognitivos 78 Motivación y Autoestima 79 Aspectos Relevantes Frente al SD 80 Triangulación 81 Capítulo IV. Resultados 84 Resultados Categorías: Diseño de la Estrategia 86 Planificación del proceso de enseñanza 86 Estrategia Didáctica mediada por las TIC 87 Recursos 90 Perfil Maestro 91 Resultados categorías: Desarrollo y aplicación de la estrategia 93 Funciones Cognitivas 93 Motivación y Autoestima 96 Aspectos Relevantes del SD 97 Capítulo V Conclusiones 99 Hallazgos 99 Recomendaciones 105 Referencia 108 Apéndices 115 Maestría This document presents the process and the application of an investigation that tried to design a didactic strategy mediated by ICT (Information and Communication Technology) to promote the learning of the addition operation to a child with Down Syndrome. As specific objectives, the development of the sum notion was first determined through a diagnostic test, then activities were designed and applied to strengthen the addition operation. Finally, through observation and the results of the strategy, its effectiveness was evaluated. This allowed for modifications to the strategy. Guided by the qualitative paradigm and having the case study as a methodological design, we sought to improve educational practices. Through the didactic strategy, the teaching and learning processes were oriented in the mathematical dimension, more specifically the addition operation, in a child with Down syndrome. The strategy highlights the importance of generating inclusion in the educational system for Down children to promote learning in mathematics and in the addition operation, this proposal being a way of intervening both in the disorder and in the learning processes. Through the strategy, the learning of an adequate mathematical notion was developed, taking into account that the disorder emphasizes cognitive and learning processes, so that the disorder is a variable that is related in the design and development of activities. This facilitated attention in virtual classes generating a significant impact on the Down child, facing the current pandemic and feeling motivated by the virtual educational context.

International audience; Several studies suggest that neurons from the lateral region of the SuM (SuML) innervating the dorsal dentate gyrus (DG) display a dual GABAergic and glutamatergic transmission and are specifically activated during paradoxical (REM) sleep (PS). The objective of the present study is to characterize the anatomical, neurochemical and electrophysiological properties of the SuML-DG projection neurons and to determine how they control DG oscillations and neuronal activation during PS and other vigilance states. For this purpose, we combine structural connectivity techniques using neurotropic viral vectors (rabies virus, AAV), neurochemical anatomy (immunohistochemistry, in situ hybridization) and imaging (light, electron and confocal microscopy) with in vitro (patch clamp) and in vivo (LFP, EEG) optogenetic and electrophysiological recordings performed in transgenic VGLUT2-cre male mice. At the cellular level, we show that the SuML-DG neurons co-release GABA and glutamate on dentate granule cells and increase the activity of a subset of DG granule cells. At the network level, we show that activation of the SuML-DG pathway increases theta power and frequency during PS as well as gamma power during PS and waking in the DG. At the behavioral level, we show that the activation of this pathway does not change animal behavior during PS, induces awakening during slow wave sleep and increases motor activity during waking. These results suggest that the SuML-DG pathway is capable of supporting the increase of theta and gamma power in the DG observed during PS and plays an important modulatory role of DG network activity during this state.

In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics. This preprint has been formally published as "Feng Qi and Chuan-Jun Huang, Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales Serie A Matematicas, Vol. 114, Paper No. 191, 9 pages (2020); available online at https://doi.org/10.1007/s13398-020-00927-y."

Glavni cilj ovog rada je analiza nepristranih igara. U tu svrhu objašnjene su neke strategije koje se javljaju u kombinatornim igrama. Kako bi pokazali posebna svojstva koje imaju nepristrane igre, definirane su pozicije i opcije u igri, te suma igara. Poseban naglasak stavljen je na igru nim pomoću koje je definirana vrijednost pod nazivom nimberi. To je klasa beskrajno malih vrijednosti koje se ne ponašaju kao nijedna vrijednost s kojima smo se do sada susreli, a poprimaju je nepristrane igre. Jedan od najbitnijih rezultata ovog rada je Sprague-grundy teorem po kojem je svaka nepristrana igra ekvivalenta nim-hrpi. Zbog toga igra nim ima veliku ulogu u analizi nepristranih igara., The main objective of this master’s thesis is the analysis of impartial games. For this purpose, some strategies that occur in combinatorial games are explained. In order to show the special properties that impartial games have, positions and options in the game are defined, as well as the sum of games. Special emphasis is placed on the game nim by which is defined the value nimbers. It is a class of infinitesimals that do not behave like any values that we have yet encountered. They occur naturally as the values of the impartial game. One of the most important results of this master’s is Sprague-grundy theorem according to which any impartial game is equivalent to a nim-heap. Therefore, nim plays a mayor role in the analysis of impartial games.

U ovom radu opisan je matematički model zvuka. Opisano je nastajanje zvuka u nekoj prostoriji na mjestu slušatelja, što podrazumijeva opis direktnog zvuka, ranih refleksija i odjeka prostorije. Uz te opise, kratko je navedeno što je to akustički komfor i kako su navedeni modeli primjenjivi u stvarnosti, te zašto je akustička obrada prostora bitna. U privitku rada nalazi se programski kod za simulator akustike prostora, a u radu su opisane metode simulacije zvuka na računalu općenito, kao i konkretna implementacija simulatora iz privitka. This paper describes a mathematical model of sound. The formation of sound in a room in the place of the listener is described, which implies a description of direct sound, early reflections and impulse response of a room. In addition to this, the paper briefly describes what acoustic comfort is and how the examples given are useful in reality, and why acoustic treatment of rooms is important. Attached to the paper is the program code for the room acoustics simulator, and the paper describes the methods of sound simulation on a computer in general, as well as the specific implementation of the simulator from the attachment.

In the paper, the authors find the sum of the Lah numbers and make sure that the Kummer confluent hypergeometric function 1F1(n+ 1; 2; z) has only n− 1real and negative zeros.