ROBUST RECURSIVE IDENTIFICATION OF HAMMERSTEIN MODELS BASED ON WEISZFALD ALGORITHM

The Hammerstein models can accurately describe a wide variety of nonlinear systems (chemical process, power electronics, electrical drives, sticky control valves). Algorithms of identification depend, among other, on the assumption about the nature of stochastic disturbance. Practical research shows that disturbances, owing the presence of outliers, have a non-Gaussian distribution. In such case it is a common practice to use the robust statistics. In the paper, by analysis of the least favourable probability density, it is shown that the robust (Huber`s) estimation criterion can be presented as a sum of non-overlapping - norm and - norm criteria. By using a Weiszfald algorithm - norm criterion is converted to - norm criterion. So, the weighted - norm criterion is obtained for the identification. The main contributions of the paper are: (i) Presentation of the Huber`s criterion as a sum of - norm and - norm criteria; (ii) Using the Weiszfald algorithm  – norm criterion is converted to a weighted - norm criterion; (iii) Weighted extended least squares in which robustness is included through weighting coefficients are derived for NARMAX (nonlinear autoregressive moving average with exogenous variable) . The illustration of the behaviour of the proposed algorithm is presented through simulations

SYSTEM IDENTIFICATION USING NEWTON–RAPHSON METHOD BASED ON SYNERGY OF HUBER AND PSEUDO–HUBER FUNCTIONS

In real situations the presence of outliers is unavoidable and that is why the distribution of a disturbance is non-Gaussian. A synthesis of an algorithm of identification based on the Newton-Raphson method is considered for this case. The method requires that the loss function should be twice differentiable. Huber loss function, relevant for the treatment of outliers, has just the first derivative. In order to overcome the problem, the pseudo- Huber loss function is introduced. This function behaves similarly to the Huber loss function and has derivatives of an arbitrary order. In this paper, the pseudo- Huber loss function is used for the second derivative of functional in the Newton-Raphson procedure. The main contributions of the paper are: (i) Design of a new robust recursive algorithm based on the synergy of Huber and pseudo – Huber functions; (ii) The convergence analysis

The bronze signum from Timacum Maius and its cultic attribution

The bronze signum discussed in this paper was discovered by archaeological ex­cavation on the site of Timacum Maius in 2010. Found in the area of a luxurious Roman-period building, the artefact shows a tapering body with a central conical socket similar to a spearhead socket. It is one of the twenty-three known signa of the so-called classical-type. Most of them were found in the context of the cult of Jupiter Dolichenus, and we also presume the cultic purpose of the bronze signum from Timacum Maius. A similar find comes from Jupiter Dolichenus’ shrine in Egeta on the Danube limes with an inscription that connects it directly with the Dolichenian cult, and with the First Cohort of Cretans (Cohors I Cretum), the unit which had previously been stationed at Timacus Maius. The signum from Timacum Maius is most likely also connected with the cult of Jupiter Dolichenus and chronologically belongs to a period which is much earlier than the Severan age

Epigraphic and Archaeological Evidence Contributing to Identifying the Location and Character of Timacum Maius

Systematic archaeological excavation in the area of the village of Niševac near Svrljig, southeast Serbia, of a Roman settlement site, possibly Timacum Maius station on the main Roman road Lissus-Naissus-Ratiaria connecting the Adriatic and the Danube, has been going on for five years. Epigraphic and etymological analysis of an inscription dedicated to Hera Sonketene (dat. Hρα Σονκητηνη) provides evidence for the possible balneological character of the entire area of Timacum Maius, which was geomorphologically similar to and connected by a road network with the Thracian region of Denteletika centred on Pautalia, where the dedicant, Tiberius Claudius Theopompus served as strategos. The archaeological evidence complements the conclusions suggested by the epigraphic material. The recently discovered secondcentury Roman structure furnished with a hypocaust system using perforated circular- sectioned pebble-filled ceramic tubuli for heating the floors and outer walls of the building may have served a balneal purpose. A sizeable Roman bathhouse, with remains of two pools and two rooms with a hypocaust and ceramic tubuli, has also been partially explored. In the broader area of Svrljig Valley (near the village of Prekonoga), a luxurious Roman villa with a marble hexagon, numerous rooms and a bath, recently subjected to a rescue excavation, has been completely cleared and recorded. The first geophysical survey on the Timacum Maius site has also been undertaken

Locating the timacum maius station on the roman road lissus-naissus-ratiaria: New archaeological research

As the exact location of two Timacum stations remains an open issue, the results of the latest archaeological investigations in the environs of Svrljig, southeast Serbia, seem to offer some corroborative evidence for the hypothesis proposed in our previous contribution that this might be the location of Roman Timacum Maius. A small-scale trial excavation was undertaken on the Roman site at Kalnica in the Niševac village area in July 2008. A trench 4 by 2m was opened in the zone of the site that had yielded plentiful fragments of building debris as well as small finds. A massive wall over 1m thick was found immediately beneath the surface. Built of bro­ken limestone and pebbles bound with lime mortar, it obviously was part of a larger structure. To the northeast of the wall was an area covered with fragmented roof tiles. The discovery of two ceramic tumuli embedded in the wall, indicating a wall-heating system so far unregistered on the representative Roman urban and settlement sites in Serbia, gives additional grounds to presume that this was a larger Roman settlement extending over an area of more than 5ha, possibly Timacum Maius, a station on the Roman road Lissus-Ratiaria-Naissus

Weapons and warrior equipment in the cultures of the Late Bronze and Early Iron Age on the territories of Serbia, Macedonia, Montenegro and Albania

Проучавање наоружања и ратничке опреме у културама бронзаног и гвозденог доба на територији централног и југоисточног Балкана није детаљније проучавано још од освита археологије на овим просторима. Поједине монографије или њихови делови у своме фокусу имале су и ово питање, али се њиме бавило или у уском предметном контексту, или пак у широком просторном контексту. Период који је обухваћен овим радом обухвата отприлике један миленијум, а реч је о позном брон- заном и старијем гвозденом добу, односно о времену између 1500/1450. године пре н.е. и 450/425. године пре н.е., тј. средњоевропске хронолошке фазе од почетка пе- риода Br C па до краја периода Ha D. Ова теза имала је за циљ израду комплексне анализе наоружања и ратничке опреме на поменутим просторима, с обзиром на то да у досадашњим радовима тој проблематици није поклањана адекватна пажња, и, да до сада овим предметима у целини није посвећена ни једна синтетска моногра- фија, или мања целовита публикација. Почетни методолошки поступак било је сакупљање већ објављене грађе са ис- траживаног подручја, али и непосредни увид у инвентар музејских збирки, тамо где је то могуће и где је такав материјал досупан. У уводном делу дати су основни по- даци о географији, топографији и геологији разматране територије, са нагласком на рудним лежиштима метала, важних у контексту производње оружја и ратничке оп- реме. Такође, детаљно су анализиране природне и историјске комуникације и пуни правци на овој територији, важни због потенцијалних продора одређених култура и транспорта/трговине одређених типова оружја у истраживаном периоду. У следећем поглављу прецизирани су и дефинисани хронолошки оквири теме, затим археолошке културе које обухватају поменути период и територију, док су на крају приказане основне класе оружја и ратничке опреме са детаљним описом примерака и основном типологијом која је коришћена у каталогу предмета. Најобимнији део рада свакако представља каталог налаза, у којем су обрађени сви одговарајући предмети, укупно њих 1.000 са проучаване територије уз тексту- ални опис и илустрацију, контекст и услове налаза, а који су класификовани по фа- зама у позно бронзано доба (фазе 1 и 2) и старије гвоздено доба (фазе 3 и 4), и даље по целинама: дефанзивна опрема (шлемови, кнемиде, оклопи и штитови), офанзи- вно оружје (секире, бодежи, мачеви, копља и стреле) и посебни налази (калупи за ливење оружја и опреме и камени брусеви). Након сакупљања грађе, извршена је анализа података, паралелно са поједи- начном анализом налаза кроз хронолошке периоде и утврђивање њиховог типа и диспозиције, као и евентулне повезаности са тадашњим археолошким културама или познатим палеобалканским племенима. У раду је предложена шема типологије оружја за наведену територију, која је или компилација већ постојећих типолошких решења за одређене врсте оружја и опреме које су биле најкомплетније и најцелис- ходније за проблематику којим се овај рад бави, или је пак предложена нова шема типологије за одређен вид оружја или опреме. Треба имати у виду да за поједи- не подкатегорије није било могуће дати предложак типологије. Примарна анализа обухватила је типолошку и хронолошку анализу, а у корелацији са просторном и контекстуалном димензијом отворила су се бројна додатна питања везана и за по- тенцијалне радионице и рударске потенцијале територије, трговачке и комуникаци- оне правце. Током позног бронзаног доба у тези је констатована појава микенског оружја и опреме из области Егеје и предложени су путеви контаката и комуникација централ- нобалканских заједница са медитеранским центрима бронзаног доба тога времена. За прелазни период констатован је јак продор централноевропских типова оружја у област Балкана, који вероватно сугеришу продор носилаца Гава комплекса ка југу, где је констатовано њихово, да тако кажемо, расипање и слабљење, вероватно ус- лед географских датости истраживане области, али су одређени примерци оружја овог регистровани и на јужним обалама Јадранског мора. Исто тако, регистроване су разлике између придошлих култура и аутохтоних популација у виду коришћења типова офанзивног оружја, па се тако мачеви изузетно ретко користе на простору где налазимо бојне секире и обрнуто. Најмањи број налаза приписан је фази 3, тако да за овај период (Ha C) нису могли да се донесу неки шири закључци. Током фазе 4 издвојене су бројне правилности, попут појаве тзв. скитских стрела са севера и истока, које се различито употребљавају у зависности од племенске припадности, дистрибуције дефанзивне опреме коју не користе сва палеобалканска племена, те дистрибуције одређених типова мачева и копаља у зависности од племенске при- падности. Исто тако, у одређеним случајевима примећено је да се оружје користи и дуже од столећа, или да долази до преправке или поправљања, а регистроване су и локалне варијанте настале по страним узорима.A study of the weapons and warrior equipment in the cultures of the Late Bronze and Early Iron Age on the territories of the Central and South-east Balkans was not subject of a detailed study since the very beginnings of archeology in this areas. Some monographs were focused completely or partially on this question, but either the object selection was very narrow or the territory was very wide. The period covered by this work includes roughly one millennium, and it talks about Late Bronze and Early Iron Age, and a time frame between 1500/1450 BC and 450/425 years BC, i.e. Central European chronological phases from the beginning of the period Br C until the end of the period of Ha D. The aim of this thesis is to develop complex analysis of weapons and warrior equipment on the territories mentioned above, since previous works did not paid adequate attention to this subject, and because of the fact that so far these cases as a whole was not committed no synthetic monograph or less comprehensive publication. The initial methodological procedure was gathering materials from the studied areas that were already published, as well as by direct accessing to the inventory of museum collections, where possible and where such material was available. The introductory section provide basic information about geography, topography and geology of the studied territory, with the accent on metal ore deposits, which are important in the context of the production of weapons and war equipment. Also, detailed analysis was paid to natural and historical communications and roads on this territory, which are important because of possible breakage of certain cultures and because of transport/trade of certain types of weapons in the investigated period. The next chapter gives us precise and detailed chronological framework about archeological cultures included by the mentioned time and territory, and, at the end, it describes basic classes of weapons and warrior equipment, including detailed description and basic typology of the items in the catalog. The most extensive part of the work, the catalog of objects, includes 1000 items from the studied territory, followed by the description, illustration, context and condition of the objects, classified in phases of Late Bronze (phases 1 and 2) and Early Iron Age (phases 3 and 4), and then by the categories: defensive equipment (helmets, greaves, armors and shields), offensive weapons (axes, daggers, swords, spears and arrows) and specific findings (molds and stone grinding wheels). After collecting the items, the analysis of the data was accomplished, along with a separate analysis of findings through chronological periods and determination of their type and disposition, as well as possible connections with the known archaeological cultures or paleo-Balkan tribes. In this part of the thesis the typology scheme of weapons on this territory is proposed, which is either a compilation of already existing typological solutions for certain types of weapons and equipment that were the most complete and most effective way for the issues that this paper deals with, or a new typology scheme was proposed for a certain type of weapon or equipment. Attention shoud be paid that that some sub-categories were not possible to provide an adequate typology. The primary analysis included the typological and chronological analysis and, correlated with spatial and contextual dimension, it opened up many other questions about the potential for workshops and mining potential of the territory, as well as trade and communication routes. This thesis ascertains the emergence of Mycenaean weapons and equipment from Aegean area in the Late Bronze Age, and it proposes roads of contacts and communication of Central Balkan community centers with Mediterranean Bronze Age centers at that time. In the transitional period strong penetration of central-European types of weapons was recorded in the Balkan region. This probably suggests penetration of the holders of Gava complex to the south, where their scattering and attenuation was determined, probably due to geographic features of the researched area, although some examples of this weaponry were also found on the south Adriatic coast. Likewise, this theses registers the differences between non newcomers culture and indigenous populations through the use of types of offensive weapons, for example, the swords were very rarely used in the area where we find the numerous examples of axes and vice versa. The least amount of objects was attributed to the phase 3, so for this period (Ha C) we could not get some broader conclusions. As for the phase 4, many regularities were separated, such as the so called Scythian arrows from the north and east, which were used differently depending on tribal affiliation, distribution of the defensive equipment that was not used by all Paleobalkanic tribes, and distribution of certain types of swords and spears, depending on tribal affiliation. Also, in certain cases it is observed that the weapon was used for more than a century, that in some cases it was remodeled or repaired, and local variations made under the influences of foreign models were also registered

Newly-discovered traces of the Roman Naissus-Ratiaria road and the problem of locating two Timacum stations

The goal of this paper is to reopen the question of and propose a solution to the as yet unresolved problem of the exact location of the Timacum stations on the Naissus-Ratiaria itinerary road. Based on plentiful material evidence it seeks to draw a more reliable picture of the Roman itinerary road and its newly-discovered traces. Also, it points to the possibility of a completely new interpretation of the itinerary sources relating to this issue. The method adopted here relies on the data contained in the Roman itineraries as well as on the archaeological and epigraphic evidence

Iron Spears of the Balkan Syginnae Type from the Central Balkans : (inspired by R. Vasić)

The paper addresses a particular type of iron spears which are found in the territory of Central Balkans in the period between the 6th and the 5th century BC, and which could broadly be classified as pike-like spears. As it follows in the paper, this particular type of iron spear is not uncommon in the wider area of European continent during the 1st millennium BC, and later it evolves into the Roman pilum, and specific Medieval pike-like spears. It seems as if both the appearance and evolution of such spears in a wider area is relatively concurrent, yet unrelated to each other, and it seems that the appearance of such spears represents a reaction to a more intensified use of defensive warfare equipment. In this paper, the aforementioned type of spear is distinguished from the Cyprian syginnae, which served as a standard for the first example published by R. Vasić back in 1996. Instead, a new and slightly revised term is proposed, containing the adjective Balkan. Such spears are frequently recorded in the Drim and Vardar river valleys and usually made of iron, while the largest examples measure more than 1,2 m in length

The Roman Station Timacum Maius (?): Evidence of Urbanization and Communications

The 2009 archaeological campaign at Niševac, eastern Serbia, has provided important evidence for the urban growth of a Roman settlement, such as drains and a section of the Roman road traversing the settlement. Along with a sumptuous structure furnished with a wall heating system discovered in 2008, the latest excavation results provide clues as to the importance of the settlement which, containing all elements of Roman urban architecture, offers further corroboration to its presumed identification as the Roman station of Timacum Maius on the Lissus-Naissus-Ratiaria road

The First Cohort of Cretans, a Roman Military Unit at Timacum Maius

Archaeological investigations on the site of Niševac (Timacum Maius) have been conducted over a period of eight successive years by the Institute for Balkan Studies in collaboration with the Centre for Tourism, Culture and Sports of Svrljig and the French Bordeaux-based Ausonius Institute. The 2014 campaign came up with nine Roman bricks stamped with inscriptions of the First Cohort of Cretans (Cohors I Cretum) built into the walls of a Roman bath. The inscriptions provide evi­dence for the character, chronology and history of the Roman settlement