Model Checking Tap Withdrawal in C. Elegans

We present what we believe to be the first formal verification of a biologically realistic (nonlinear ODE) model of a neural circuit in a multicellular organism: Tap Withdrawal (TW) in \emph{C. Elegans}, the common roundworm. TW is a reflexive behavior exhibited by \emph{C. Elegans} in response to vibrating the surface on which it is moving; the neural circuit underlying this response is the subject of this investigation. Specifically, we perform reachability analysis on the TW circuit model of Wicks et al. (1996), which enables us to estimate key circuit parameters. Underlying our approach is the use of Fan and Mitra's recently developed technique for automatically computing local discrepancy (convergence and divergence rates) of general nonlinear systems. We show that the results we obtain are in agreement with the experimental results of Wicks et al. (1995). As opposed to the fixed parameters found in most biological models, which can only produce the predominant behavior, our techniques characterize ranges of parameters that produce (and do not produce) all three observed behaviors: reversal of movement, acceleration, and lack of response

Global entrainment of transcriptional systems to periodic inputs

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. The basic mathematical results needed from contraction theory are proved in the paper, making it self-contained

Temporal Precedence Checking for Switched Models and its Application to a Parallel Landing Protocol

This paper presents an algorithm for checking temporal precedence properties of nonlinear switched systems. This class of properties subsume bounded safety and capture requirements about visiting a sequence of predicates within given time intervals. The algorithm handles nonlinear predicates that arise from dynamics-based predictions used in alerting protocols for state-of-the-art transportation systems. It is sound and complete for nonlinear switch systems that robustly satisfy the given property. The algorithm is implemented in the Compare Execute Check Engine (C2E2) using validated simulations. As a case study, a simplified model of an alerting system for closely spaced parallel runways is considered. The proposed approach is applied to this model to check safety properties of the alerting logic for different operating conditions such as initial velocities, bank angles, aircraft longitudinal separation, and runway separation

Bounded Verification with On-the-Fly Discrepancy Computation

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing reachtubes from simulations. In this paper, we eliminate this requirement by presenting an algorithm for computing piece-wise exponential discrepancy functions. The algorithm relies on computing local convergence or divergence rates of trajectories along a simulation using a coarse over-approximation of the reach set and bounding the maximal eigenvalue of the Jacobian over this over-approximation. The resulting discrepancy function preserves the soundness and the relative completeness of the verification algorithm. We also provide a coordinate transformation method to improve the local estimates for the convergence or divergence rates in practical examples. We extend the method to get the input-to-state discrepancy of nonlinear dynamical systems which can be used for compositional analysis. Our experiments show that the approach is effective in terms of running time for several benchmark problems, scales reasonably to larger dimensional systems, and compares favorably with respect to available tools for nonlinear models.Comment: 24 page

Simulation-based reachability analysis for nonlinear systems using componentwise contraction properties

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of trajectories of the system and next establish bounds on the convergence or divergence between the samples and neighboring trajectories. We compute these bounds using contraction theory and reduce the conservatism by partitioning the state vector into several components and analyzing contraction properties separately in each direction. Among other benefits this allows us to analyze the effect of constant but uncertain parameters by treating them as state variables and partitioning them into a separate direction. We next present a numerical procedure to search for weighted norms that yield a prescribed contraction rate, which can be incorporated in the reachability algorithm to adjust the weights to minimize the growth of the reachable set

Lagrangian Reachabililty

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201

Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight by Oscillation Synchronization

This paper describes a fully decentralized nonlinear control law for spinning tethered formation flight, based on exploiting geometric symmetries to reduce the original nonlinear dynamics into simpler stable dynamics. Motivated by oscillation synchronization in biological systems, we use contraction theory to prove that a control law stabilizing a single-tethered spacecraft can also stabilize arbitrary large circular arrays of spacecraft, as well as the three inline configuration. The convergence result is global and exponential. Numerical simulations and experimental results using the SPHERES testbed validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics

Magnetic Anisotropy and Relaxation of Pseudotetrahedral [N2O2] Bis Chelate Cobalt II Single Ion Magnets Controlled by Dihedral Twist Through Solvomorphism

The methanol solvomorph 1 amp; 8201; amp; 8901; amp; 8201;2MeOH of the cobalt II complex [Co LSal,2 amp; 8722;Ph 2] 1 with the sterically demanding Schiff base ligand 2 [1,1 amp; 8242; biphenyl] 2 ylimino methyl phenol HLSal,2 amp; 8722;Ph shows the thus far largest dihedral twist distortion between the two chelate planes compared to an ideal pseudotetrahedral arrangement. The cobalt II ion in 1 amp; 8201; amp; 8901; amp; 8201;2MeOH exhibits an easy axis anisotropy leading to a spin reversal barrier of 55.3 amp; 8197;cm amp; 8722;1, which corresponds to an increase of about 17 amp; 8201; induced by the larger dihedral twist compared to the solvent free complex 1. The magnetic relaxation for 1 amp; 8201; amp; 8901; amp; 8201;2MeOH is significantly slower compared to 1. An in depth frequency domain Fourier transform FD FT THz EPR study not only allowed the direct measurement of the magnetic transition between the two lowest Kramers doublets for the cobalt II complexes, but also revealed the presence of spin phonon coupling. Interestingly, a similar dihedral twist correlation is also observed for a second pair of cobalt II based solvomorphs, which could be benchmarked by FD FT THz EP

Todellista asiakasarvoa luomassa – myynnistä arvomyyntiin : case Mediamaisteri Oy

Tämän opinnäytetyön tavoite oli case-yritys Mediamaisteri Oy:n B2B-myyntiprosessin kehittäminen. Tarkoitus oli hyödyntää palvelumuotoilua lisäämään asiakasymmärrystä ja tukemaan asiakkaiden kokeman arvon muodostumista sekä positiivisten asiakaskokemusten syntymistä myyntiprosessin alkuvaiheen asiakaskohtaamisissa. Lisäksi tarkoitus oli kiteyttää empiirisen aineiston pohjalta saatu tieto asiakasprofiileiksi, joita voidaan hyödyntää asiakaslähtöisten ratkaisujen suunnittelussa heti asiakkuuden alusta ja ensimmäisestä myyntitapaamisesta lähtien. Opinnäytetyön tutkimuksellisen osuuden toteuttamisen pohjana on kvalitatiivinen tutkimusote ja palvelumuotoilun prosessi. Tutkimuskohde tarkennettiin kuvaamalla Mediamaisteri Oy:n asiakkuuden alkuvaiheen palvelupolku, josta rajattiin tutkimuksen kohteeksi ensimmäinen asiakastapaaminen ja sitä edeltävä aika, jolloin asiakas kiinnostuu yrityksen palveluista ja ensikontakti yritykseen tapahtuu. Tutkimusaineisto muodostuu kuudesta Mediamaisteri Oy:n yritysasiakkaan haastattelusta, jotka toteutettiin virtuaalisesti teemahaastattelun muodossa. Aineiston analysoinnissa hyödynnettiin induktiivista sisällönanalyysiä. Opinnäytetyön teoreettinen viitekehys rakentuu B2B-myynnin, asiakasarvon muodostumisen ja positiivisen asiakaskokemuksen teorioista. Opinnäytetyön empiirisessä osassa kuvataan yksityiskohtaisesti työn toteuttaminen ja toteutuksen vaiheittainen eteneminen. Opinnäytetyön tuloksien mukaan Mediamaisteri Oy:n yritysasiakkaan positiivinen asiakaskokemus palvelujen hankintavaiheessa ja ensimmäisen asiakastapaamisen aikana koostuu myyjäyrityksen koetusta osaamisesta ja ammattitaidosta, palveluasenteesta, asiakaslähtöisyydestä, vuorovaikutustaidoista, yhteistyötaidoista, avoimuuden ja luottamuksen tunteen herättämisestä ja projektinhallinnasta. Opinnäytetyön tutkimusaineiston pohjalta kerätty asiakastieto kiteytettiin Mediamaisteri Oy:n yritysasiakkaan asiakasprofiileiksi, joita voidaan tulevaisuudessa hyödyntää yrityksen asiakaslähtöisen myyntiprosessin kehittämisessä suuntaamaan toimintaa kohti todellista asiakasarvoa asiakkuuden alkuvaiheesta alkaen. Voidaan todeta, että opinnäytetyön tuloksilla on yhteyttä opinnäytetyön viitekehyksessä esitettyyn aikaisempaan teoreettiseen tietoon B2B-myynnistä, asiakasarvon muodostumisesta ja positiivisesta asiakaskokemuksesta. Opinnäytetyön tuloksissa ilmeni, että asiakasymmärryksen tavoittelu jää palvelujen hankintavaiheessa ja ensimmäisessä asiakastapaamisessa usein pinnalliselle tasolle. Jatkotutkimus etenkin vuorovaikutustaitojen merkityksestä B2B-myyntiprosessin alussa ja ensimmäisessä B2B-myyntitapaamisessa arvonluonnin ja arvomyynnin edellyttämän asiakasymmärryksen saavuttamiseksi on suositeltavaa.The aim of this thesis was to develop the B2B sales process of the case company Mediamaisteri Oy. The purpose was to utilize service design to promote the customer insight and to support the formation of the customer value and positive customer experiences in customer touchpoints during the early stages of the sales process. In addition, the purpose was to crystallize the information obtained from the empirical data into customer profiles that can be used to design customer-oriented solutions right from the beginning of a customer relationship and the initial B2B sales meeting. The basis for carrying out the empirical part of the thesis was the qualitative research and the process of service design. The research subject was defined by describing the business client’s customer journey in the beginning of the customer relationship with Mediamaisteri Oy, and by focusing to the initial B2B sales meeting and the time when the client became interested in the company's services and made the first contact. The research material consisted of six interviews of Mediamaisteri Oy's business clients, made as online theme interviews. The material was analyzed by utilizing inductive content analysis. The theoretical framework of the thesis was based on the theories of B2B sales, customer value creation and positive customer experience. In the empirical part of the thesis, the implementation of the work and the steps of the process are described in detail. The findings of the thesis indicate that the positive customer experience of a Mediamaisteri business client during the procurement phase and the initial B2B sales meeting consists of proven expertise and professionalism, service attitude, customer orientation, interaction skills, co-operation skills, openness and trust, and the project management. The research data collected was crystallized into the business client profiles of Mediamaisteri Oy, which can be used in the future to develop the customer-oriented sales process of the company in order to direct the business towards the real customer value starting right from the beginning of the customer relationship. It can be concluded that the results of the thesis are related to the previous theoretical knowledge of B2B sales, customer value creation and a positive customer experience presented in the theoretical framework of the thesis. The results of the thesis showed that the pursuit of customer understanding during the procurement phase and the initial B2B sales meeting often remains superficial. Further research on the significance of interaction skills in the beginning of the sales process and at the initial B2B sales meeting is desirable to achieve value creation and value-based customer insight