Uso dell'algebra Max-Plus nella costruzione di portafogli di copertura ottimali

In questa tesi, ci occupiamo di risolvere una classe di problemi di Finanza matematica nei quali è necessario avere un portafoglio che abbia sempre valore maggiore di una barriera data dal mercato, detta ostacolo. È questo il caso di un portafoglio di copertura di un'opzione americana, dell'assicurazione di portafogli o in generale di situazioni in cui il mercato imponga vincoli, per esempio di tipo legale. L'investitore deve essere in grado, in ogni istante, di corrispondere a chi ha acquistato l'opzione o a chi ha assicurato il portafoglio il suo valore attuale, o in generale di non infrangere alcuna regola. Se il portafoglio avesse un valore troppo basso, sarebbe necessario aggiungere capitale; per tutelarsi da questa evenienza, è quindi opportuno seguire una strategia che permetta di avere un portafoglio con valore sempre sufficientemente grande. Inoltre, una volta soddisfatto questo vincolo, è auspicabile cercare la strategia ottimale, che permetta cioè di ottenere il maggior guadagno possibile. Supporremo che il mercato sia completo e senza opportunità di arbitraggio.\par Dal punto di vista matematico, si modellizza un mercato come un processo stocastico a valori in $R^ extrm{d}$, che rappresenta il modo in cui i prezzi siano soggetti a variabilità. Di conseguenza, anche l'opzione da coprire, o in generale l'ostacolo, è rappresentato da un processo stocastico. Le ipotesi fatte sulla natura del mercato ci consentiranno, a meno di cambiare misura di probabilità, di ricondurci a una situazione in cui tutti i portafogli autofinanziati sono delle martingale. par Per rappresentare la condizione di ottimalità, bisogna considerare che ogni investitore ha una disponibilità diversa ad assumersi dei rischi con la prospettiva di un guadagno, che varia con l'ammontare del capitale investito: esiste cioè una funzione che associa al valore del portafoglio un'utilità per l'investitore. Trovare il portafoglio ottimale significa allora in termini matematici trovare la martingala tale che se la si compone con la funzione di utilità si ottiene un processo con speranza massima. Il problema consta dunque di due parti: egin{enumerate} item [1)] definire l'insieme $mathcal{M}$ delle martingale che dominano un processo dato (l'ostacolo); item [2)] trovare la martingala ottimale (rispetto alla funzione di utilità) di questo insieme. end{enumerate} par La prima parte viene fatta utilizzando la teoria degli inviluppi di Snell. par La seconda parte invece viene risolta utilizzando al posto dei numeri reali l'algebra Max-Plus $R_{max}$, cioè $Rcup{-infty}$ dotato delle operazioni $max$ e $+$. In questo semicampo, sarà costruita una decomposizione per supermartingale simile a quella di Doob-Meyer, effettuata però rispetto all'operazione $max$: $$M^{MP}_tgeqmax(Z_t,A_t) ,$$ per una data supermartingala $Z$ e con un opportuno processo opzionale $A$. Applicheremo questa decomposizione all'inviluppo di Snell dell'ostacolo, ottenendo così il portafoglio candidato a essere ottimale.par Per dimostrare che si tratta effettivamente della scelta migliore, faremo vedere come da ipotesi naturali sulla funzione di utilità si ottenga che essa è concava. Utilizzeremo quindi l'ordine stocastico concavo $leq_{cv}$, che ordina un insieme di variabili aleatorie ${X_i}_{iinLambda}$ nel senso che $$X_ileq_{cv}X_jquad extrm{se}quadforall f:R ightarrowR extrm { concava}quadE[f(X_i)]leqE[f(X_j)] ,$$ se $E[f(X_i)]$ è definito, e dimostreremo che la martingala $M^{MP}$ è la martingala più grande rispetto a questo ordine.par Nella parte finale, ci occuperemo di mostrare come sia possibile con questo metodo svolgere calcoli completi per ricavare esplicitamente la strategia ottimale. Questo nostro metodo ha il vantaggio di poter essere applicato fino al risultato esplicito anche con ipotesi sulla funzione di utilità quasi inesistenti: questo significa poterlo applicare a quasi tutte le preferenze di investimento pur senza conoscerle in dettaglio. Osserviamo infatti che la funzione di utilità personale, in quanto caratterizzante le scelte di un investitore, spesso non viene dettagliatamente esplicitata

Residual Stress Mapping of GRCop-84 Fabricated by SLM

No abstract availabl

FFPred 3: feature-based function prediction for all Gene Ontology domains

Predicting protein function has been a major goal of bioinformatics for several decades, and it has gained fresh momentum thanks to recent community-wide blind tests aimed at benchmarking available tools on a genomic scale. Sequence-based predictors, especially those performing homology-based transfers, remain the most popular but increasing understanding of their limitations has stimulated the development of complementary approaches, which mostly exploit machine learning. Here we present FFPred 3, which is intended for assigning Gene Ontology terms to human protein chains, when homology with characterized proteins can provide little aid. Predictions are made by scanning the input sequences against an array of Support Vector Machines (SVMs), each examining the relationship between protein function and biophysical attributes describing secondary structure, transmembrane helices, intrinsically disordered regions, signal peptides and other motifs. This update features a larger SVM library that extends its coverage to the cellular component sub-ontology for the first time, prompted by the establishment of a dedicated evaluation category within the Critical Assessment of Functional Annotation. The effectiveness of this approach is demonstrated through benchmarking experiments, and its usefulness is illustrated by analysing the potential functional consequences of alternative splicing in human and their relationship to patterns of biological features

Scalable web services for the PSIPRED Protein Analysis Workbench

Here, we present the new UCL Bioinformatics Group’s PSIPRED Protein Analysis Workbench. The Workbench unites all of our previously available analysis methods into a single web-based framework. The new web portal provides a greatly streamlined user interface with a number of new features to allow users to better explore their results. We offer a number of additional services to enable computationally scalable execution of our prediction methods; these include SOAP and XML-RPC web server access and new HADOOP packages. All software and services are available via the UCL Bioinformatics Group website at http://bioinf.cs.ucl.ac.uk/

Signalling properties at single synapses and within the interneuronal network in the CA1 region of the rodent hippocampus

Understanding how the complexity of connections among the neurons in the brain is established and modified in an experience- and activity-dependent way is a challenging task of Neuroscience. Although in the last decades many progresses have been made in characterising the basic mechanisms of synaptic transmission, a full comprehension of how information is transferred and processed by neurons has not been fully achieved. In the present study, theoretical tools and patch clamp experiments were used to further investigate synaptic transmission, focusing on quantal transmission at single synapses and on different types of signalling at the level of a particular interneuronal network in the CA1 area of the rodent hippocampus. The simultaneous release of more than one vesicle from an individual presynaptic active zone is a typical mechanism that can affect the strength and reliability of synaptic transmission. At many central synapses, however, release caused by a single presynaptic action potential is limited to one vesicle (univesicular release). The likelihood of multivesicular release at a particular synapse has been tied to release probability (Pr), and whether it can occur at Schaffer collateral\u2013CA1 synapses, at which Pr ranges widely, is controversial. In contrast with previous findings, proofs of multivesicular release at this synapse have been recently obtained at late developmental stages; however, in the case of newborn hippocampus, it is still difficult to find strong evidence in one direction or another. In order to address this point, in the first part of this study a simple and general stochastic model of synaptic release has been developed and analytically solved. The model solution gives analytical mathematical expressions relating basic quantal parameters with average values of quantities that can be measured experimentally. Comparison of these quantities with the experimental measures allows to determine the most probable values of the quantal parameters and to discriminate the univesicular from the multivesicular mode of glutamate release. The model has been validated with data previously collected at glutamatergic CA3-CA1 synapses in the hippocampus from newborn (P1-P5 old) rats. The results strongly support a multivesicular type of release process requiring a variable pool of immediately releasable vesicles. Moreover, computing quantities that are functions of the model parameters, the mean amplitude of the synaptic response to the release of a single vesicle (Q) was estimated to be 5-10 pA, in very good agreement with experimental findings. In addition, a multivesicular type of release was supported by various experimental evidences: a high variability of the amplitude of successes, with a coefficient of variation ranging from 0.12 to 0.73; an average potency ratio a2/a1 between the second and first response to a pair of stimuli bigger than 1; and changes in the potency of the synaptic response to the first stimulus when the release probability was modified by increasing or decreasing the extracellular calcium concentration. This work indicates that at glutamatergic CA3-CA1 synapses of the neonatal rat hippocampus a single action potential may induce the release of more than one vesicle from the same release site. In a more systemic approach to the analysis of communication between neurons, it is interesting to investigate more complex, network interactions. GABAergic interneurons constitute a heterogeneous group of cells which exert a powerful control on network excitability and are responsible for the oscillatory behaviour crucial for information processing in the brain. They have been differently classified according to their morphological, neurochemical and physiological characteristics. In the second part of this study, whole cell patch clamp recordings were used to further characterize, in transgenic mice expressing EGFP in a subpopulation of GABAergic interneurons containing somatostatin (GIN mice), the functional properties of EGFPpositive cells in stratum oriens of the CA1 region of the hippocampus, in slice cultures obtained from P8 old animals. These cells showed passive and active membrane properties similar to those found in stratum oriens interneurons projecting to stratum lacunosum-moleculare. Moreover, they exhibited different firing patterns which were maintained upon membrane depolarization: irregular (48%), regular (30%) and clustered (22%). Paired recordings from EGFP-positive cells often revealed electrical coupling (47% of the cases), which was abolished by carbenoxolone (200 mM). On average, the coupling coefficient was 0.21 \ub1 0.07. When electrical coupling was particularly strong it acted as a powerful low-pass filter, thus contributing to alter the output of individual cells. The dynamic interaction between cells with various firing patterns may differently control GABAergic signalling, leading, as suggested by simulation data, to a wide range of interneuronal communication. In additional paired recordings of a presynaptic EGFP positive interneuron and a postsynaptic principal cell, trains of action potentials in interneurons rarely evoked GABAergic postsynaptic currents (3/45 pairs) with small amplitude and slow kinetics, and that at 20 Hz exhibited short-term depression. In contrast, excitatory connections between principal cells and EGFP-positive interneurons were found more often (17/55 pairs) and exhibited a frequency and use-dependent facilitation, particularly in the gamma band. In conclusion, it appears that EGFP-positive interneurons in stratum oriens of GIN mice constitute a heterogeneous population of cells interconnected via electrical synapses, exhibiting particular features in their chemical and electrical synaptic signalling. Moreover, the dynamic interaction between these interneurons may differentially affect target cells and neuronal communication within the hippocampal network

Impact assestment of open-ended laboratory activities on TOL and TOLC-I engineering entrance test performances

LAUREA MAGISTRALENei paesi sviluppati si riscontra una marcata carenza di laureati nei settori di scienze, tecnologia, ingegneria e matematica, nonostante la crescente domanda in questi ambiti professionali. Gli elevati tassi di abbandono nei primi anni di istruzione superiore, in particolare nei corsi di fisica, rappresentano una sfida rilevante. Questa tendenza è spesso causata da una preparazione insufficiente e da un’approccio tradizionale basato su lezioni frontali. Diversi studi evidenziano che il coinvolgimento attivo durante l’insegnamento ed un approccio maggiormente incentrato sugli studenti migliori i risultati di apprendimento e interesse. I laboratori ’open-ended’ rappresentano un esempio di tale approccio: a differenza dei laboratori convenzionali, essi favoriscono l’esplorazione indipendente e il coinvolgimento attivo dei partecipanti, stimolando le capacità di problem-solving e contribuendo a esperienze di apprendimento più profonde. La seguente analisi ha indagato l’impatto di un corso di orientamento basato su attività di laboratorio open-ended sulle prestazioni degli studenti nei test d’ingresso ingegneristici. Il gruppo in esame è composto da studenti di quarta e quinta superiore provenienti da diverse scuole, partecipanti ai test d’ingresso TOL e TOLC-I presso il Politecnico di Milano nel 2023. Due analisi principali sono state condotte: un test del χ2 (between-subject design) e un’analisi dei gain sui punteggi (within-subject design). I risultati del test del χ2 hanno evidenziato una significativa correlazione tra i fattori, confrontando gli studenti esposti al trattamento con quelli che non lo hanno ricevuto. Questi risultati sono stati confermati ottimizzando le proporzioni della composizione dei gruppi e ulteriormente supportati dalle misurazioni di odds ratio e Cramer’s V. L’analisi dei gain sui punteggi ha evidenziato risultati positivi, soprattutto per specifiche categorie di studenti, nonostante una significativa incertezza che ha complicato l’interpretazione diretta. Complessivamente, i risultati suggeriscono che il corso di orientamento con attività di laboratorio ’open-ended’ abbia un impatto positivo sulle prestazioni degli studenti, specialmente all’interno di determinati sottogruppi.Developed countries face a significant shortage of science, technology, engineering and mathematics graduates, despite the rising demand. High dropout rates in the early years of higher education, particularly in academic physics courses, are a major issue, often due to inadequate preparation and traditional lecture-based teaching. Several research studies show that active student engagement and student-centered approaches enhance learning outcomes, attendance and engagement. Specifically, open-ended laboratory approaches, unlike conventional methods, immerse students in real-world challenges, enhancing autonomy and problem-solving skills. This method encourages independent exploration and innovative solutions, promoting deeper and more immersive learning experiences. Our analysis investigated whether an orientation course, comprising open-ended laboratory activities, contributed in producing significant improvements in students’ performance on engineering entrance exams. The group under investigation was formed by fourth and fifth-year high school students from various institutes participating the TOL and TOLC-I engineering entrance exams at Politecnico di Milano in 2023. Two primary analyses were conducted: a χ2 test (between-subject design) and a gain score analysis (within-subject design). The χ2 test results indicated a significant correlation between factors when comparing students exposed to the treatment with those who did not. These findings were validated by refining group composition proportions and confirmed through odds ratio and Cramer’s V effect size measurements. The gain score analysis also showed positive results, particularly for specific subgroups, despite considerable uncertainty that introduced challenges for direct interpretation. Overall, the findings suggest that the orientation course incorporating open-ended laboratory activities positively impacts student performance, especially within certain subgroups

Exploring the Healthcare Needs and Experiences of Legally Blind Adults

The objective of this project is to describe the healthcare needs and experiences of legally blind adults. There are more than 3.4 million Americans, forty years and older, that are visually impaired. Evidence shows that legally blind older adults are more likely to have medical problems than sighted older adults. This study utilizes a qualitative design using in-depth interviews. Four participants were recruited through social networks. Interviews were audio-recorded and transcribed verbatim. Text was analyzed for recurrent themes and ideas. Themes found include a loss of self-dignity, safety and quality issues, and the importance of disability competent care and empowerment

Giovanna Minneci, Senior Art Exhibition Portfolio

This is work created for the Senior Art Exhibition Portfolio 2024.https://digitalcommons.snc.edu/artportfolios/1085/thumbnail.jp

Isolation and Comparative Transcriptome Analysis of Human Fetal and iPSC-Derived Cone Photoreceptor Cells.

Loss of cone photoreceptors, crucial for daylight vision, has the greatest impact on sight in retinal degeneration. Transplantation of stem cell-derived L/M-opsin cones, which form 90% of the human cone population, could provide a feasible therapy to restore vision. However, transcriptomic similarities between fetal and stem cell-derived cones remain to be defined, in addition to development of cone cell purification strategies. Here, we report an analysis of the human L/M-opsin cone photoreceptor transcriptome using an AAV2/9.pR2.1:GFP reporter. This led to the identification of a cone-enriched gene signature, which we used to demonstrate similar gene expression between fetal and stem cell-derived cones. We then defined a cluster of differentiation marker combination that, when used for cell sorting, significantly enriches for cone photoreceptors from the fetal retina and stem cell-derived retinal organoids, respectively. These data may facilitate more efficient isolation of human stem cell-derived cones for use in clinical transplantation studies