We generalize bistellar operations (often called flips) on simplicial manifolds to a notion of general flips on PL-spheres. We provide methods for computing the cd-index of these general flips, which is the change in the cd-index of any sphere to which the flip is applied. We provide formulas and relations among flips in certain classes, paying special attention to the classic case of bistellar flips. We also consider questions of "flip-connecticity", that is, we show that any two polytopes in certain classes can be connected via a sequence of flips in an appropriate class.

<p style="text-align: justify;">Betain je bioaktivno jedinjenje, koje ima značajne fiziolo&scaron;ke funkcije u čovekovom organizmu kao osmolit i donor metil grupa za mnoge biohemijske procese. Endogena sinteza betaina je uglavnom nedovoljna da zadovolji potrebe organizma te je zbog toga neophodan njegov unos preko hrane. Žitarice predstavljaju glavni izvor betaina u ljudskoj ishrani. Jedan od načina da se poveća unos betaina u ljudskoj ishrani je preko funkcionalne hrane obogaćene betainom. Prema regulativi evropskog udruženja cerealija za doručak (European Breakfast Cereal Association) iz 2012. god. (Commission Regulation (EU) No 432/2012) dozvoljeno je deklarisanje zdravstvene izjave za prehrambene proizvode koji sadrže najmanje 500 mg betaina po porciji (40g flips proizvoda) uz navođenje napomene da se zdravstveni efekti mogu očekivati ukoliko se dnevno unese 1500 mg betaina. Zdravstvena izjava glasi: &bdquo;betain doprinosi normalnom metabolizmu homocisteina&ldquo;. Povećano interesovanje za zdravu ishranu dovelo je do veće potražnje za alternativnim žitaricama, gde spelta zbog svojih biolo&scaron;kih, agronomskih, prehrambenih i medicinskih karakteristika kao i bogatih nutritivnih svojstava, zauzima značajno mesto. Glavni cilj ove teze je bila optimizacija ekstrudiranja i proizvodnje funkcionalnog flips proizvoda od speltinog integralnog bra&scaron;na sa dodatkom betaina na dvopužnom ekstruderu. Prvi put je u procesu prehrambenog ekstrudiranja primenjena analiza vi&scaron;eciljne optimizacije u kombinaciji sa neuronskim mrežama i genetskim algoritmom kako bi se dobio maksimalan sadržaj betaina u flips proizvodu pri minimalnoj potro&scaron;nji specifične mehaničke energije. Definisan je nov funkcionalni proizvod sa betainom koji bi potencijalno pro&scaron;irio asortiman flips proizvoda na trži&scaron;tu i utvrđene su njegove fizičke, funkcionalne, teksturalne, reolo&scaron;ke i senzorske osobine. Sadržaj betaina i potro&scaron;nja specifične mehaničke energije su ključni izlazi koji predstavljaju konkurentne ciljeve u procesu ekstrudiranja. Za proizvodnju flips proizvoda pobolj&scaron;anog nutritivnog kvaliteta i funkcionalnog profila koji sadrži od 1601,6 do 1764,7 mg betaina u 40 g (čime se i zadovoljava preporučeni dnevni unos betaina) i kome odgovara potro&scaron;nja specifične mehaničke energije od 97,4 do 114,1 Wh/kg optimalni su sledeći procesni parametri: protok materijala od 20,45 do 24,04 kg/h, vlaga materijala od 18,6 do 19,44 % i brzina obrtanja pužnice od 250 obrtaja u minuti. Da bi se dobili pouzdani rezultati za sadržaj betaina u spelti i flips proizvodima razvijena je, optimizovana i validovana metoda tečne hromatografije visokih perfomansi. Metoda je uspe&scaron;no primenjena i u analizi betaina u žitaricama, pseudožitaricama i njihovim proizvodima.</p> / <p>Betaine is a bioactive compound that has significant physiological functions in the human organism as an osmolite and methyl group donor for many biochemical processes. The endogenous synthesis of betaine is generally insufficient to satisfy the requirements of the organism, therefore its intake is necessary through the food. Cereals are the main sources of betaine in human nutrition. One of the ways to increase betaine intake in human nutrition is through betaine enriched functional foods. In the 2012 European Union Regulation (Commission Regulation (EU) No 432/2012), it is permissible to declare a health statement for foods containing at least 500 mg betaine per portion (40g of extruded product), stating that the health effects can be expected if 1500 mg of betaine are consumed on a daily basis. The health statement states: &quot;Betaine contributes to the normal metabolism of homocysteine.&quot; Increased interest in healthy food has led to the higher demand for alternative cereals, where spelt takes a significant place due to its biological, agronomic, nutritional and medical characteristics, as well as its rich nutritional properties. The main goal of this work was the optimization of extrusion and production of the functional snack product from spelt wholegrain flour with the addition of betaine which is performed on twin-screw extruder. According to our best knowledge, there was no investigation in which the multi-objective optimization (MOO) analysis coupled with artificial neural network and genetic algorithm was applied to the extrusion cooking process in order to achieve simultaneously maximum betaine content and minimum energy consumption in the snack spelt product. A new functional snack product that can potentially expand the range of snack products and its physical, functional, textural, sensory and rheological properties were defined. The betaine content and specific mechanic energy are the key outputs that represent competing objectives in the extrusion proces. To produce snack product with improved nutritive quality and functional profile which contains betaine content from 1601,6 to 1764,7 mg/40g, which would contribute to the recommended daily intake of betaine, correspond to specific mechanical energy from 97,4 to 114,1 Wh/kg, following optimal parameters were obtained: feed rate from 20,45 to 24,04 kg/h, moisture content from 18,6 to 19,44 % and screw speed at 250 rpm. Also, optimization, development and validation of the high pressure liquid chromatographic method for measuring betaine content in spelt and snack products was also designed and applied.</p>

Master of Science / We are in an ever-increasing demand for computing power to sustain our technological advancements. A significant driving factor of our progress is the size and speed of memory we possess. Modern computer architectures use DDR4-based DRAM (Dynamic Random Access Memory) to hold all the immediate information for processing needs. Each bit in a DRAM memory module is implemented with a tiny capacitor and a transistor. Since the capacitors are prone to charge leakage, each bit must be frequently rewritten with its old value. A dedicated memory controller handles the periodic refreshes. If the cells aren't refreshed, the bits lose their charge and lose the information stored by flipping to either 0 or 1 (depending upon the design). Due to manufacturing variations, every tiny capacitor fabricated will have different physical characteristics. Charge leakage depends upon capacitance and other such physical properties. Hence, no two DRAM modules can have the same properties and decay pattern and cannot be reproduced again accurately. This DRAM attribute can be considered a source of 'Physically Unclonable Functions' and is sought after in the Cryptography domain. This thesis aims to characterize the decay patterns of commercial DDR4 DRAM modules. I implemented a custom System On Chip on AMD/Xilinx's ZCU104 FPGA platform to interface different DDR4 modules with a primitive memory controller (without refreshes). Additionally, I introduced electric and magnetic fields close to the DRAM module to investigate their effects on the decay characteristics.

<p dir="ltr">We study the communication model with perfect feedback considered by Berlekamp (PhD Thesis, 1964), in which Alice wishes to communicate a binary message to Bob through a noisy adversarial channel, and has the ability to receive feedback from Bob via an additional noiseless channel. Berlekamp showed that in this model one can tolerate 1/3 fraction of errors (a.k.a., bit-flips or substitutions) with non-vanishing communication rate, which strictly improves upon the 1/4 error rate that is tolerable in the classical one-way communication setting without feedback. In the case when the channel is corrupted by erasures, it is easy to show that a fraction of erasures tending to 1 can be tolerated in the noiseless feedback setting, which also beats the 1/2 fraction that is maximally correctable in the no-feedback setting. In this thesis, we consider a more general perfect feedback channel that may introduce both errors and erasures. We show the following results:</p><p dir="ltr">1. If α, β ∈ [0, 1) are such that 3α + β < 1, then there exists a code that achieves a positive communication rate tolerating α fraction of errors and β fraction of erasures. Furthermore, no code can achieve a positive-rate in this channel when 3α + β ≥ 1.</p><p dir="ltr">2. For the case when 3α + β < 1, we compute the maximal asymptotic communication rate achievable in this setting.</p>

En la presente memoria, se abordan cuatro problemas, existiendo en todos ellos una gran interacción entre la combinatoria y la geometría. El primer problema que se estudia es la introducción de varias extensiones del concepto de tipo de orden para nubes de puntos. Concretamente, se introducen los tipos de orden circulares y triángulares, en las versiones orientada y no orientada. Se han demostrado resultados combinatorios análogos a resultados bien conocidos sobre tipos de orden ordinarios, introducidos por Goodman y Pollack como es el llamado Teorema de ordenación geométrica. Se ha estudiado también la información geométrica que proporciona cada uno de estos conceptos. El segundo problema estudia el empaquetamiento plano de grafos; esto es, el trazado de grafos, disjuntos en aristas, en el plano. Hemos obtenido varios resultados sobre el empaquetamiento plano de árboles y ciclos. Concretamente, para árboles que no sean estrellas, se ha demostrado que siempre admiten empaquetamiento plano: dos copias de un árbol cualquiera, un árbol cualquiera y un camino, un árbol cualquiera y un ciclo. También se han obtenido resultados sobre empaquetamiento plano de dos o tres ciclos. La principal herramienta que se ha utilizado es la representación de un árbol en un polígono convexo con propiedades muy concretas. En tercer lugar se estudia el grafo T (P) de árboles geométricos de una nube de puntos P, siendo este grafo el que tiene por vértices los árboles generadores sin cortes de P y dos de tales árboles T1, T2 son aduacentes si y sólo s, T2C=t1e+f para ciertas aristas e y f. Se han obtenido propiedades combinatorias de estos grafos, especialmente en el caso particular en que el conjunto de puntos esta en posición convexa. En este caso se ha determinado el centro, radio y grupo de automofismos de estos grafos, y demostrado que son hamiltonianos y de conectividad máxima. Finalmente, también se ha estudiado el grafo Mm de los emparejamientos perfectos sin cortes de una nube de 2m puntos en posición convexa. Entre los resultados obtenidos cabe destacar que se ha demostrado que Mm es bipartito, hamiltoniano sólo si m es par y que el diámetro de Mm es igual a m-1, siendo todos los emparejamientos de excentricidad máxima.

[pt] Nessa tese, consideramos coberturas de regiões tridimensionais por dominós, especialmente as da forma D x [0,N]. Em particular, nós investigamos as componentes conexas do espaço de coberturas desse tipo de região por flips, o movimento local que consiste em remover dois dominós paralelos adjacentes e colocá-los de volta na única outra posição possível. Para regiões da forma D x [0,2], nós definimos um invariante polinomial Pt(q) que caracteriza coberturas que estão quase na mesma componente conexa, num sentido discutido na tese. Também provamos que o espaço de coberturas desse tipo de região é conexo por flips e trits, um movimento local que consiste em remover três dominós adjacentes e ortogonais entre si e colocá-los de volta na única outra posição possível. No caso geral, o invariante é um inteiro, o twist, para o qual damos uma fórmula combinatória simples, bem como uma interpretação via teoria dos nós; também provamos que o twist tem propriedades aditivas para decomposições adequadas de uma região. Por fim, investigamos também o conjunto de valores que são twists de coberturas de uma caixa L x M x N. / [en] In this thesis, we consider domino tilings of three-dimensional regions, especially those of the form D x [0,N]. In particular, we investigate the connected components of the space of tilings of such regions by ips, the local move performed by removing two adjacent dominoes and placing them back in the only other possible position. For regions of the form D x [0,2], we define a polynomial invariant Pt(q) that characterizes tilings that are \ almost in the same connected component , in a sense discussed in the thesis. We also prove that the space of domino tilings of such a region is connected by ips and trits, a local move performed by removing three adjacent dominoes, no two of them parallel, and placing them back in the only other possible position. For the general case, the invariant is an integer, the twist, to which we give a simple combinatorial formula and an interpretation via knot theory; we also prove that the twist has additive properties for suitable decompositions of a region. Finally, we investigate the range of possible values for the twist of tilings of an L x M x N box.