In this work, we deal with fixed interval scheduling problems with the possibility of random delay of the end of the tasks (FIS). First, we pre- sent the basic deterministic FIS problems and ways to solve them. Next, we introduce the concept of minimax and present two well-known and one new FIS problem under uncertainty, when random task delays are conside- red to belong to a certain uncertainty set. Next, we deal with the solution of previously presented FIS problems for five chosen uncertainty sets. We present both previously achieved and original results. The work concludes with a summary of a numerical study of two problems. First, we explore the possibility of Lagrange relaxation application to the first presented problem. Next we explore the quality of approximation allowing to solve the later of problems as LP. 1

California Quail were exposed to fixed-interval schedules whose values ranged from FI 90 to FI 180. Post-reinforcement pause lengths and terminal rates were recorded and grouped into relative frequency distributions. The relative post-reinforcement pause length was found to be an increasing function of FI value such that at larger FI values a proportionally greater period of time was taken up by the post-reinforcement pause. Terminal rate (rate during the final 20% of the interval) was a decreasing function of FI value. The large amounts of variability in terminal rates observed indicated that terminal rate in fixed-interval schedules is not constant from interval to interval as is often reported in the literature. For a given subject, when overall rate of response for a session was plotted as a function of mean pause length for that session, no consistent relationship was found. Among the subjects there were two to three-fold differences in overall rate on FI 90, the only value to which all subjects were exposed. Differences among subjects in mean overall rates were correlated with differences in mean pause lengths, however. Thus, a subject's performance on a fixed-interval schedule could be characterized in terms of pause length and overall rate although rate in any given session was not necessarily correlated with mean pause length for that session, Differences between subjects in mean overall rates were also correlated with differences in mean terminal rates.

abstract: Theories of interval timing have largely focused on accounting for the aggregate properties of behavior engendered by periodic reinforcement, such as sigmoidal psychophysical functions and their scalar property. Many theories of timing also stipulate that timing and motivation are inseparable processes. Such a claim is challenged by fluctuations in and out of states of schedule control, making it unclear whether motivation directly affects states related to timing. The present paper seeks to advance our understanding of timing performance by analyzing and comparing the distribution of latencies and inter-response times (IRTs) of rats in two fixed-interval (FI) schedules of food reinforcement (FI 30-s and FI 90-s), and in two levels of food deprivation. Computational modeling revealed that each component was well described by mixture probability distributions embodying two-state Markov chains. Analysis of these models revealed that only a subset of latencies are sensitive to the periodicity of reinforcement, and pre-feeding only reduces the size of this subset. The distribution of IRTs suggests that behavior in FI schedules is organized in bouts that lengthen and ramp up in frequency with proximity to reinforcement. Pre-feeding slowed down the lengthening of bouts and increased the time between bouts. When concatenated, these models adequately reproduced sigmoidal FI response functions. These findings suggest that behavior in FI fluctuates in and out of schedule control; an account of such fluctuation suggests that timing and motivation are dissociable components of FI performance. These mixture-distribution models also provide novel insights on the motivational, associative, and timing processes expressed in FI performance, which need to be accounted for by causal theories of interval timing. / Dissertation/Thesis / Masters Thesis Psychology 2015

The present study contributes an apparatus and research paradigm useful in generating human performances sensitive to concurrent schedules of reinforcement. Five participants produced performances observed to be under temporal and ratio control of concurrent fixed interval-fixed ratio schedules. Two aspects of interaction between FI and FR schedules were distinguishable in the data. First, interaction between two schedules was observed in that changes in the value of one schedule affected behavior reinforced on another schedule. Second, switching from one pattern to the other functioned as an operant unit, showing stability during schedule maintenance conditions and sensitivity to extinction. These effects are discussed in the context of current views on behavior under concurrent schedules of reinforcement, and some implications for the conceptualization, measurement, analysis, and treatment of complex behavior are presented.

Orientador: Prof. Dr. Marcelo Salvador Caetano / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Neurociência e Cognição, 2016. / Em um esquema de reforço de múltiplos intervalos fixos, diferentes intervalos de tempo são sinalizados por diferentes estímulos ambientais que adquirem controle sobre o comportamento. Trabalhos anteriores no nosso laboratório mostraram que o desempenho temporal é controlado não só por estímulos externos, mas também por aspectos temporais da tarefa de acordo com a ordem na qual os diferentes intervalos ¿ misturados em todas as tentativas ou em blocos de várias tentativas ¿ são treinados. Este projeto de pesquisa visa descrever as condições de treino sob as quais os estímulos assumem controle sobre o comportamento dos ratos numa tarefa de estimação temporal. As variáveis manipuladas são o número de pares de estímulo-intervalo treinados (Experimento I), o tamanho do bloco de tentativas repetidas de cada par de estímulo-intervalo (Experimento II) e a ordem de apresentação das condições de treino em bloco e misturado (Experimento III). Os resultados encontrados sugerem que o desempenho temporal dos animais na tarefa foi controlado por regularidades temporais e não pelos estímulos externos disponíveis quando treinados em blocos de várias tentativas consecutivas com o mesmo par de estímulo-intervalo. Ainda, que alguns animais parecem deixar de usar os estímulos externos como pista preditiva do intervalo quando a ordem de apresentação passa de treino misturado para treino em bloco. Uma possível explicação para estes resultados é que as pistas temporais sombreiam os estímulos visuais pelo controle do desempenho temporal. Estes resultados com ratos têm sido expandidos e observados em estudos com humanos, portanto os resultados deste projeto têm relevância no entendimento de estratégias de aprendizagem que podem ser aplicadas ao comportamento humano. / In a multiple fixed intervals schedule of reinforcement, different time intervals are signaled by different environmental stimuli which acquire control over behavior. Previous work in our lab has shown that temporal performance is controlled not only by external stimuli, but also by temporal aspects of the task depending on the order in which the different intervals ¿ intermixed across trials or in blocks of several trials ¿ are trained. The aim of this project was to describe the training conditions under which the stimuli acquire control over temporal performance. We manipulated the number of stimulus-interval pairs trained (Experiment I), the number of consecutive trials of each stimulus-interval pair per training block (Experiment II), and the order in which the two training types are presented - in blocks then intermixed, and vice-versa (Experiment III). The results suggest that, when trained in blocks of several consecutive trials of the same stimulus-interval pair, temporal performance was controlled by temporal regularities across trials and not by the external stimuli available. Moreover, some animals seem to stop relying on the external stimuli as predictive cues of the intervals when the training condition changes from intermixed to blocked. One possible account for those data is that temporal cues overshadow visual stimuli for the control of temporal performance. Similar results have also been observed in human studies, which suggest that temporal regularity is a salient cue used to guide behavior in temporal tasks across species.

This thesis is focused on the fixed interval scheduling (FIS) problems with random delays. Firstly, we introduce the concept of FIS problems and the exogenous and endogenous uncertainty. In the next chapter we will summarize the FIS problems under decision dependent randomness and their relation to the robust coloring. We will extend previous results with proposing a new FIS problem with maintenance. This problem is a specific case of a decision-dependent probabilities as it allows to use a specific type of a job - the maintenance, which positively impacts the probability distributions of job delays. We start with defining a problem, where maintenance must be assigned only before regular jobs and then we propose the general case, when maintenances appears during the whole processing period. We show why this approach leads to an optimal solution and provide a detailed example of a small problem.We also discuss some extensions of our problem. Finally, we conduct a numerical study. We solve the FIS maintenance problem with the Cplex solver for a few different settings of inputs. It seems that the maintenance is useful only for certain settings, such as jobs with high probability of having a delay or the price of outsourcing being much higher than the cost of maintenance. It is also shown that the problem...

Physical activity is an important health-related behavior, and The Centers for Disease Control and Prevention (CDC) recommends that children engage in at least 60 minutes of moderate-to-vigorous-physical activity (MVPA) daily (CDC, 2015). However, worldwide, many children do not reach those requirements and health problems associated with physical inactivity are becoming more prevalent (CDC, 2015; World Health Organization [WHO], 2016). Recently, a few studies have conducted an intervention analysis to evaluate implications for function-based interventions to increase physical activity (Larson, Normand, Morley, & Miller, 2014; Zerger, Normand, Boga, & Patel, 2016). However, intervention analyses, indicate an overall decrease in levels of MVPA. This limitation could hinder further improvements of function-based interventions to increase physical activity, and is thus important to investigate. The current study partially replicated Zerger et al. (2016), and investigated the effects of alternating FA test conditions and repeated presentation of single condition exposure on maintenance of levels of MVPA in children. Additionally, the current study also evaluated the effectiveness of a more intermittent contingent schedules of reinforcement (i.e., fixed-interval limited-hold schedule) during intervention conditions. Results suggest it might be beneficial for caretakers and parents to deliver reinforcement in the form of social reinforcement to increase MVPA in preschool children. Additionally, the data suggest to promote MVPA, a more intermittent schedule of contingent social reinforcement does not reliably promote stable levels of MVPA.

This thesis concerns solutions to problems that arise in optimizing fixed interval scheduling under situations of uncertainty such as when there are random delays in job process times. These problems can be solved by using a vertex coloring with random edges and problems can be formulated using integer linear, quadratic and stochastic programming. In this thesis is propo- sed a new integer linear formulation. Under certain conditions there is proved its equivalence with stochastic formulation, where is maximized the schedule reliability. Moreover, we modified the proposed formulation to obtain bet- ter corresponding to real life situations. In a numerical study we compared computational time of individual formulations. It turns out that the propo- sed formulation is able to solve scheduling problems considerably faster than other formulations. 1

Made available in DSpace on 2016-04-29T13:18:00Z (GMT). No. of bitstreams: 1 Dissertacao Thais Martins Sales.pdf: 1293785 bytes, checksum: 6161405c79ed51ec0c3dacacebe67ee1 (MD5) Previous issue date: 2006-05-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study was an attempt to investigate possible relations between responding that is reinforced according to schedules based on a temporal parameter and performing other activities to which no reinforcement contingencies are programmed. These activities have been called adjunctive behavior, collateral behavior or interim activities. Two questions guided this study: a) is there any difference in response rate, average time between reinforcers, and percentage of reinforced responses when an FI schedule or a DRL schedule is in force, if the subject can engage in other activities; b) are typical sequential patterns developed between responses when these schedules are in force? Four male food deprived rats were subjects of this experiment. The apparatus was an experimental box with seven chambers in which subjects could perform different activities, such as bar pressing, eating, running, drinking, and wood-chewing. For two subjects, bar pressing was reinforced according to three DRL schedules (DRL 4s, DRL 5s, and DRL 20s). One of the subjects was first kept in the chamber with the bar and food dispenser and then was allowed to access the other chambers, the other was first allowed to access the other chambers and then was kept in the chamber with the bar and food dispenser. For the other two subjects, bar presses were reinforced according to two FI schedules (FI 5s and FI 10s). One of the subjects first had access to all chambers and then was kept in the chamber with the bar and food dispenser, and the other was kept in the chamber with the bar and food dispenser during the whole experiment. Bar presses, reinforcement deliveries, and occupancy of chambers were recorded. Results show there was a difference in response rate, average time between reinforcers, and percentage of reinforced responses in both schedules, depending on the access condition, mainly when responses were reinforced according to schedules higher than FI 5s and DRL 4s. Higher response rates, lower average time between reinforcers and higher percentage of reinforced responses were observed for the DRL subjects when access was possible than when it was not possible, and higher response rates, higher average time between reinforcers and higher percentage of reinforced responses were observed for the FI subjects when access was possible than when it was not possible. No typical sequential patterns were observed when access was possible and either of the two studied schedules was in force. Results are discussed in terms of possible controlling variables to performing activities other than bar pressing when responding is being reinforced according to FI and DRL schedules / O presente trabalho é uma tentativa de investigação de possíveis relações entre o responder reforçado segundo dois esquemas de reforçamento que envolvem parâmetros temporais e o engajamento em atividades para as quais não há reforço programado, chamadas de atividades ínterim, comportamento adjuntivo ou comportamento colateral. Duas perguntas dirigiram a realização deste trabalho: a) há diferença na taxa de respostas, tempo médio entre reforços e porcentagem de respostas reforçadas segundo esquemas DRL e FI, caso haja possibilidade de engajamento em outras atividades? e b) alguma seqüência típica de engajamento em outras atividades é formada no intervalo entre respostas reforçadas segundo estes esquemas? Os sujeitos do experimento foram quatro ratos machos privados de alimento. Foi utilizada uma caixa experimental com sete compartimentos, nos quais era possível o engajamento em diferentes atividades: pressionar a barra, comer, beber, correr, roer madeira. Dois sujeitos tiveram as respostas de pressão à barra reforçadas segundo esquemas DRL com três valores diferentes (4s, 9s e 20s). Um deles passou, primeiro, por uma condição na qual o acesso a todos os compartimentos era permitido, chamada de aberta, e, segundo, por uma condição na qual era mantido no compartimento onde havia a barra e o comedouro, chamada de fechada, e o outro sujeito passou, primeiro, pela condição fechada e, segundo, pela condição aberta. Os outros dois sujeitos tiveram as respostas de pressão à barra reforçadas segundo esquemas FI com dois valores diferentes (5s, 10s). Um sujeito passou primeiro pela condição aberta e, depois, pela condição fechada e o outro passou apenas pela condição fechada. As pressões à barra, os reforços e a permanência nos compartimentos foram registrados. Os resultados mostraram que houve diferença na taxa de respostas, tempo médio entre reforços e porcentagem de respostas reforçadas em função da condição de acesso, especialmente quando as respostas de pressão à barra foram reforçadas segundo o esquema DRL 9s e DRL 20s, para os dois primeiros sujeitos, e segundo o FI 10s, para os outros dois sujeitos. Na condição aberta com esquema DRL em vigor, observou-se uma menor taxa de respostas, menor tempo entre reforços e maior porcentagem de respostas reforçadas do que na condição fechada, com o mesmo esquema em vigor. Na aberta com esquema FI em vigor, observou-se uma menor taxa de respostas, maior tempo entre reforços e maior porcentagem de respostas reforçadas do que na condição fechada, com o mesmo esquema em vigor. Seqüências típicas de engajamento em outras atividades não foram observadas quando o acesso era possível e o responder era reforçado segundo os esquemas FI e DRL. Os resultados são discutidos em termos de possíveis variáveis que controlam o engajamento em outras atividades, quando respostas são reforçadas segundo estes dois esquemas

本研究利用兩種時間關聯之操作式制約行為作業探討韁核的行為功能，一為區辨性增強低頻反應作業（簡稱DRL作業），另一為固定時距作業（簡稱FI作業）。本研究以神經毒素鵝膏蕈酸（ibotenic acid）破壞韁核的方式來測試大白鼠受試在上述行為作業之不同歷程的影響效果，包含習得歷程、行為表現階段以及已習得後轉換得酬賞之反應標準等三個階段。實驗一的結果顯示破壞韁核對於DRL作業的習得歷程具有明顯的影響，其影響效果在DRL短時距作業中造成無法以有效率的壓桿反應模式獲得酬賞；反之，破壞操弄的效果並不影響FI長與短時距作業的習得歷程。實驗二的結果顯示破壞韁核並不影響已習得的DRL作業與FI作業的行為表現，兩項作業的實驗組受試皆能維持穩定的行為反應模式且與控制組無明顯差異。實驗三對已習得的DRL行為進行時距參數的轉換（含調高及降低兩部份），結果顯示破壞韁核之操弄並未明顯的影響這項轉換新的時距之作業要求，但實驗組受試的確比控制組較遲緩達到新的時距要求。綜合而言，本研究以專屬性較高的神經毒素破壞韁核，用較多元指標的行為分析方式探討韁核的行為功能；其結果發現韁核參與DRL行為內含的區辨學習與對於錯誤偵測的負向迴饋，這些功能是需要透過韁核與其他中腦及邊緣系統的組織互動。 / This study examined the function of habenula (Hb) by two kinds of operant conditioned behavior tasks based on temporal contingency, including the differential reinforcement of low-rate responding (DRL) task and fixed-interval (FI) task. The effects of Hb lesion induced by neurotoxin ibotenic acid were examined at the different stages of operant conditioned behavior, including acquisition, performance, and transition stages. The results showed that bilateral lesions of Hb did not affect the locomotor activity and the basic lever-pressing. In Experiment 1, Hb lesion group had less reinforced responses and lower peak time indicating the deficits of acquisition of the DRL task. In contrast, the same lesion manipulation on the FI task did not produce any difference between the lesion group and the control group. The data of Experiment 2 showed that Hb lesion did not significantly affect the learned behavior maintained on DRL-10s or FI-30s schedule. In Experiment 3, Hb lesion produced a subtle, but not significant, impairment on behavioral transition from a learned interval to a newly-set interval (upward or downward). The lesioned subjects made a slower transition than the controls. In conclusion, these data suggest that the function of habenula is involved in discrimination learning and error detection for acquiring DRL behavior. However, it is likely that these Hb functions have to rely upon dynamic relationship between Hb and other midbrain limbic systems.