LP, MIP and QP models, data input/output, user graphs, heuristics

Multiple MIP solutions, infeasibility handling, data transfer in memory, remote execution, XML and JSON data formats, solver tuning

Piecewise linear, approximation, SOS, SOS1, SOS2, SOS-1, SOS-2, Special Ordered Set, pwlin, pws, step function, piecewise linear function

general constraints, boolvar, logctr, Boolean variables, logical expressions, minimum value, maximum value, absolute value

indicator constraints, logic constraints, logctr

simple LP problem, graphical representation of results

simple MIP problem, random generation of data, use of model parameters, setting Optimizer controls

simple LP problem, formulation of blending constraints

simple MIP problem

simple MIP problem, semi-continuous variables, graphical representation of results

MIP problem solved by column generation, working with multiple problems, using 'sethidden', setting Optimizer and Mosel control parameters

MIP problem, implementation of Branch-and-Cut and Cut-and-Branch algorithms, definition of Optimizer callbacks, Optimizer and Mosel parameter settings, 'case', 'procedure', 'function', time measurement

MIP problem, graphical solution representation, re-solving with modified bounds, data input from file, dynamic arrays for data and decision variables, use of 'exists', model cuts

simple IP problem, formulation of knapsack constraints, model parameters, function 'random'

LP or MIP problem, formulation of resource constraints and material balance constraints, formatted solution printing, if-then-else, if-then-elif statements

MIP problem, alternative formulation with SOS-1, tricky formulation of resource use profiles and calculation of benefits, graphical solution representation

MIP problem, modeling a piecewise linear function with SOS-2, graphical representation of data

simple LP problem, using dynamic arrays for data and decision variables, formatted output printing, inline 'if', format of data files

MIP problem, loop over problem solving, TSP subtour elimination algorithm; procedure for generating additional constraints, recursive subroutine calls, working with sets, 'forall-do', 'repeat-until', 'getsize', 'not', graphical representation of solutions

MIP problem, modeling an equivalence; sparse data format, graphical output representation, 'if-then-else'

Simple LP problem, single period production planning

simple MIP problem, formulation of balance constraints using inline 'if'

2 MIP problems with different objectives, data preprocessing, incremental definition of data array, encoding of arcs, logical 'or' (cumulative version) and 'and', 'procedure' for printing solution, 'forall-do', 'max', 'finalize', graphical representation of results, 'sin', 'cos'

MIP problem, encoding of arcs, 'range', 'exists', 'create', algorithm for printing paths, 'forall-do', 'while-do', 'round', graphical representation of results

MIP problem, encoding of paths, 'finalize', 'getsize'

MIP problem, formulation of constraints to eliminate inadmissible subtours, definition of model cuts, selection with '|', algorithm for printing the tours, graphical solution representation

MIP problem, formulation with extra nodes for modes of transport; encoding of arcs, 'finalize', union of sets, nodes labeled with strings, graphical solution representation

MIP problem, encoding of arcs, 'range', formulation of sequencing constraints

MIP problem, formulation of constraints to exclude subcycles, graphical representation of results

MIP problem, alternative formulation using SOS1, graphical solution representation

MIP problem, formulating disjunctions (BigM); 'dynamic array', 'range', 'exists', 'forall-do', graphical solution representation

MIP problem, representation of multi-period production as flow; encoding of arcs, 'exists', 'create', 'isodd', 'getlast', inline 'if'

MIP problem, algorithm for data preprocessing; file inclusion, 3 nested/recursive procedures, working with sets, 'if-then', 'forall-do', 'exists', 'finalize'

MIP problem, data preprocessing, algorithm for preemptive scheduling that involves looping over optimization, ''Gantt chart'' printing and drawing

MIP problem with 3 different objectives; 'procedure' for solution printing, 'if-then'

MIP problem, many specific constraints, tricky (pseudo-) objective function, 'finalize'

LP solving, solution printout, array and set data structures

MIP solving, binary variables, index set types, logic constraints

Dynamic creation of variables, formulation of resource constraints

MIP problem

MIP problem

MAXSAT model

use of 'exists', finalization of index sets

Retrieving and displaying IIS

LP, MIP, NLP problem formulations, solution reporting, graphical display, multiple problems, iterative solution algorithms

dynamic package loading, model compilation, BIM file

Access to files on remote (parent or child) nodes

Initializing sets, set operations, set comparison

Generating online documentation for Mosel models and packages

Recursive function calls; using 'readln'

The 'if-then-elif-then' selection statement

Using the 'forall' loop

Nested loops: repeat-until, while, while-do

File access, using 'readln', 'fskipline'

Text parsing functionality

Nested loops: repeat-until, forall-do, while-do

Recursive subroutine calls, overloading of subroutines

Definition of subroutines, data structures list and record, type definition

Submodel included in model source, datablock, deployment as executable

deployment as executable, deployment via scripts

Using xprnls, generating dictionary files

Remote model execution in debugging mode, implementation of a debugger

Remote model execution in profiling mode, decoding of profiling and coverage results

Simple access routines - adding nodes, recursive display of subtrees

Retrieving XML nodes using xpath search expressions; modifying and formatting XML files

Parsing documents with unknown structure

Processing a text file into a different text format, generating Mosel code, deployment as executable

Definition of subroutines, data structures of union types, type definition, JSON parsing

handling I/O errors during data input

Using and combining 'count' and 'as counter'

Local declaration of entities, array aliasing

array initialization, indexation, sparse array, array dimensions, array size

Lists: initialization, enumeration, operators, access functions

list operators, list handling routines

Defining and initializing records

Working with record data structures

Defining a user type with a record

defining unions, type any, specifying union type, initialization of unions from/to text format files, reference to operator

Subroutine definition, overloading, recursive function calls, function return values, variable number of arguments, subroutine references, mmreflect

real number format, text formatting

Debugging and profiling commands, parallel debugging

Using sparse arrays, dynamic array, ahsmap array

Implementing subroutines, overloading, using packages

Implementing packages, defining namespaces, namespace search, namespace groups

Implementing packages, version management, deprecation, annotations

Types 'text', 'textarea', 'parsectx'; text parsing

Accessing annotations from a model or host application

Using documentation annotations, moseldoc tool

Enumeration of sparse data, exists

Comparison tolerance

Model exit code

Preprocessing source code, preprocessor symbol, positioning markers

Find or start AEC2 instance, start Mosel, model execution

Variable creation, using 'sethidden', working with multiple problems

Adding constraints and cuts, using the cut manager, run-time parameters

Working with bases, saving and loading MIP solutions

Working with submodels, record data structures

Changing constraint type, redefining the objective

Multiple objectives, configuration of objectives

Redefinition of constraints

Dynamic arrays for data and decision variables, formatting output

Using module nlsolv

Using the optnode callback or the cut manager callback, addcuts, storecuts and loadcuts, subroutine reference

Solving a sequence of CP subproblems, in-memory data exchange

Parallel and sequential solving of subproblems

CP target values, MIP start solution, MIP callbacks, cutting plane algorithm

Parallel computing, distributed computing, distributed architecture, in-memory data exchange, shmem, job queue, events, detach submodel, clone submodel

Concurrent subproblem solving, coordination via events, in-memory data exchange, mempipe, mempipe notifications, remote mempipe

Multiple concurrent submodels, events, in-memory data exchange

Sequential and parallel submodel execution, loading partial MIP start solutions, model cloning, shared data

Iterative sequential submodel solving, nonlinear subproblem, MIQP formulation

Solution heuristic, parallel submodel execution

Multiple problem runs, submodel

Names generation, variable name, constraint name, location information, compilation options, loading names, public declaration

mmxprs command, Xpress Solver command line, running matrix file

Evolutionary algorithm, iterative LP solving

Working with subproblems, iterative LP solving

2-stage stochastic program, scenario-based robust optimization

Iterative submodel runs, in-memory data exchange

Iterative solving, recursion, SLP

quadratic constraints and objective

Discrete variables

Discrete variables

Quadratic constraints

Nonlinear objective

Approximation of a function

Trigonometric functions

Nonlinear objective

Nonlinear constraints and objective

Nonlinear objective and constraints

Trigonometric constraints and objective

Quadratic constraints and quadratic objective

Nonlinear constraint and objective, alternative objective functions

Quadratic constraints

Quadratic constraints

Nonlinear objective

Nonlinear constraints, trapezoidal discretization

SOCP formulation

Trigonometric constraints, graphical representation

Discretization, GNUPlot graphic, subroutine references

NLP, alternative solvers

Defining robust constraints, uncertainty sets, nominal values

Types of uncertainty sets

'ellipsoid' uncertainty set, retrieving the worst value of an uncertain

'scenario' and 'cardinality' uncertainty sets

'scenario' and polyhedral uncertainty sets

polyhedral uncertainty set

'cardinality' uncertainty set

polyhedral uncertainty set

Regression analysis, data exchange with R, evaluating R functions from Mosel

Logistic regression, data exchange with R, evaluating R functions from Mosel, graph drawing with R

Accessing data sources (text, spreadsheets, databases)

Using 'initializations to' with 'evaluation of'

XML and JSON data formats, generation of HTML

Data input, initializations from, SQL, ODBC, spreadsheet, CSV

Data output, initializations to, SQL, ODBC, spreadsheets, CSV

dataframe, union types, CSV format

array types, noindex

auto-indexation

solution data output, 'evaluation of'

data input/output, multiple tables, multiple data arrays

Advanced SQL functionality, retrieve database and table structure

record data structure, list data structure

Types any, date, time; data input/output

data types date, time, datetime

Multidimensional array input, option partndx

'mmodbc.odbc', 'mmsheet.excel', 'mmetc.diskdata' I/O drivers, SQL, XML, JSON

'bin', 'shmem', 'raw', 'text', 'tmp', 'rmt' I/O drivers

Queued execution of remote models with result graphic

Iterating over MIP solves, graphical representation of solution values

Lines with simple styling, recursive subroutine calls

Points and polylines with various styling options

Graphical objects rectangle and text, simple styling

Graphical objects pie and text, simple styling

Graphical objects rectangle and text, simple styling, reading free-format input text data file, animation

Points and polylines, pausing display, intercepting window closing, animation, image inclusion

Retrieving matrix coefficient ranging information, getscale, SVG graph drawing

Find or start AEC2 instance, start Mosel, model execution

Binary data format

Remote model execution, file manager, events

Remote execution of multiple Mosel models

Remote model execution, data exchange between remote nodes

Distributed computing, concurrent submodel execution, job queue, events

Parallel execution of submodels, parallel execution of submodels, stopping submodels

Parallel execution of submodels, Java solution graph

Submodel execution, events, bindrv binary format, in-memory data I/O

Model compilation, parameterized model execution, matrix output, accessing results

Model compilation

Accessing sets, arrays, lists, records; retrieving solution information

Display information and contents of models and libraries

Stopping a model run

Compilation to/from memory; data input/output in memory; redirect output using the 'cb' driver

Using the debugger interface

Compile/load/run models, retrieve information about model objects, redirect model output

Data exchange during model execution

Using the Xpress Optimizer library with Mosel

Using the 'mem' I/O driver

'cb', 'bin', 'mem', 'raw', 'sysfd' I/O drivers

Model compilation, parameterized model execution, matrix output, accessing results

Accessing sets, arrays, lists, records; retrieving solution information

Display information and contents of models and libraries

Compilation to/from memory; data input/output in memory; redirect output using the 'java' driver

Using the debugger interface

Compile/load/run models, retrieve information about model objects, redirect model output

Data exchange during model execution

Using the 'java' I/O driver

Model compilation, parameterized model execution

Parameterized model execution, data exchange in memory

LP solving, start Mosel from a VBA script in Excel, data input from Excel

MIP solving, start and interrupt Mosel from a VBA script in Excel, Mosel output to Excel

Compile/load/run models, redirect model output

Model compilation, parameterized model execution, matrix output, accessing results

Accessing sets, arrays, lists, records; retrieving solution information

Display information and contents of models and libraries

Compilation to/from memory; data input/output in memory

Compile/load/run models, retrieve information about model objects, redirect model output

Data exchange during model execution

Using C#

Accessing sets and arrays; retrieving solution information; displaying information and contents of models and libraries; Compilation to/from memory; data input/output in memory

Defining integer, real, string, boolean constants

Implementing a subroutine

Defining an external type with operators

Defining an external type with operators and access routines; defining module parameters and services

Defining an external type with operators and access routines; defining module parameters and services

Defining external types with operators

Using the NI matrix handling functionality, extending a type, defining parameters and subroutines, defining a callback function

Using the mmnl matrix handling functionality, extending a type, defining parameters and subroutines, defining a callback function

Module embedded in a C program

Defining I/O drivers

Defining an I/O driver

Creating a static module

Using 'all_different', enumerating all feasible solutions, SVG graphs showing progress of solving

Using 'all_different', formatted solution printout

Formulation of a scheduling problem with MIP and CP

Subtour elimination algorithm

MIP and CP formulations for discrete feasibility problems

Multiple problem runs, comparison, blog

LP, MIP and QP models, explicit initialization, index sets, heuristic solution

Using Xpress callbacks

Using the change branch callbacks

Changing bounds, accessing solver controls

Saving/loading bases, changing objective coefficients

Changing RHS coefficients, working with bases

Using the MIP log callback

Changing bounds

Load LP problem, adding a constraint

Retrieving solution values and tree search information

Using the optnode callback, saving/loading bases, changing bounds

Retrieve basic variables and their names, btran

Adding rows and columns, branching directives

Using the solution enumerator and MIP solution pool

Using the solution enumerator and MIP solution pool

Using repairinfeas

Lexicographic goal programming using the Xpress multi-objective API

Piecewise linear, approximation, SOS, SOS1, SOS2, SOS-1, SOS-2, Special Ordered Set, piecewise linear function

general constraints, minimum value, maximum value, absolute value

indicator constraints, logic constraints

MIP, indicator constraints

Defining different types of constraints

Nonlinear constraints

Multi-objective solving

Stating quadratic constraints

Defining semi-continuous variables

Working with subproblems, modifying constraints

Using Xpress callbacks

MIP, indicator constraints

Defining different types of constraints

Nonlinear constraints

Multi-objective solving

Stating quadratic constraints

Defining semi-continuous variables

Working with subproblems, modifying constraints

Looping of optimization, using the cut manager

Data structures arrays and collections

MIP modeling, binary fixing heuristic, quadratic constraints, infeasibility handling

Minimum value constraints and absolute value constraints

Nonlinear constraints, trapezoidal discretization

Constraint formulation options

Constraint redefinition, multiple problems

Nonlinear constraints

Binary variables, SOS definition

Formulation of resource constraints and material balance constraints

Defining SOS-2, pwl, piecewise linear

Iterative solving, modify constraint definitions

Formulation of a scheduling problem with indicator constraints

Loading a MIP start solution

Using the message callback

Using IIS

Using the solution enumerator and MIP solution pool

Using the solution enumerator and MIP solution pool

Modify a problem by adding extra rows and columns

Lexicographic goal programming using the Xpress multi-objective API

Using Xpress callbacks

Changing bounds, accessing solver controls

Using the MIP log callback

Load LP problem, adding a constraint

Retrieving solution values and tree search information

Using the optnode callback, saving/loading bases, changing bounds

Retrieve basic variables and their names, btran

Using the change branch callbacks

Using repairinfeas

Changing bounds

Saving/loading bases, changing the objective

Saving/loading bases, changing right-hand side values

MIP, indicator constraints

Defining different types of constraints

Multi-objective solving

Stating quadratic constraints

Defining semi-continuous variables

Working with subproblems, modifying constraints

Looping of optimization, using the cut manager

Collections data structure

MIP modeling, binary fixing heuristic, quadratic constraints, infeasibility handling

Constraint formulation options

Nonlinear constraints

Binary variables, SOS definition

Formulation of resource constraints and material balance constraints

Defining SOS-2, pwl, piecewise linear constarints

Iterative solving, modify constraint definitions

Loading a MIP start solution

Using Xpress callbacks

Changing bounds, accessing solver controls

Using IIS

Using the MIP log callback

Load LP problem, adding a constraint

Using the solution enumerator and MIP solution pool

Using the solution enumerator and MIP solution pool

Retrieving solution values and tree search information

Lexicographic goal programming using the Xpress multi-objective API

Changing bounds, accessing solver controls

Using IIS

Using the MIP log callback

Load LP problem, adding a constraint

Using the solution enumerator and MIP solution pool

Using the solution enumerator and MIP solution pool

Retrieving solution values and tree search information

Using token lists to express nonlinear formulas

Using string based formulas to express nonlinear formulas

Providing initial values to nonlinear variables

Implementing complex user functions returning their own derivatives

Implementing user functions

Using strings to express nonlinear formulas, including a 'map' userfunction

Using strings to express nonlinear formulas, including a 'vecmap' userfunction

Using strings to express nonlinear formulas, including a 'multimap' userfunction

Using strings to express nonlinear formulas, including a 'mapdelta' userfunction

Using strings to express nonlinear formulas, including a 'vecmapdelta' userfunction

Using strings to express nonlinear formulas, including a 'multimapdelta' userfunction

Using strings to express nonlinear formulas

Using strings to express nonlinear formulas, including a 'map' userfunction

Using strings to express nonlinear formulas, including a 'vecmap' userfunction

Using strings to express nonlinear formulas, including a 'vecmapdelta' userfunction

Using strings to express nonlinear formulas, including a 'mapdelta' userfunction

Using strings to express nonlinear formulas, including a 'multimap' userfunction

Using strings to express nonlinear formulas, including a 'multimapdelta' userfunction

Using strings to express nonlinear formulas

Using strings to express nonlinear formulas, including a 'map' userfunction

Using strings to express nonlinear formulas, including a 'vecmap' userfunction

Using strings to express nonlinear formulas, including a 'vecmapdelta' userfunction

Using strings to express nonlinear formulas, including a 'mapdelta' userfunction

Using strings to express nonlinear formulas, including a 'multimap' userfunction

Using strings to express nonlinear formulas, including a 'multimapdelta' userfunction

Convexity

Numerical differentiaton

Local optimality

Dual multipliers

Non-connected feasible regions

Feasiblity breakers

Penalty multipliers

Support sets

Step bounding

Zero placeholders

Piecewise linear, approximation, SOS, SOS1, SOS2, SOS-1, SOS-2, Special Ordered Set, piecewise linear function

general constraints, minimum value, maximum value, absolute value

indicator constraints, logic constraints

Using NumPy arrays

Using the newnode callback

Using Irreducible Infeasible Sets

Loading a problem directly

Modelling using Python objects

Changes to a problem

Extending a problem

Using NumPy and Xpress

Basis handling and sensitivity methods

Building quadratic expressions

Building quadratic expressions

Building quadratic expressions

Solving a problem multiple times

Model with indicators

Model with special ordered sets

Using Xpress callbacks

Using Xpress callbacks

Writing and reading a problem to disk

Writing and reading a problem to disk

MIP problem with binary variables

Puzzle modeling

Modelling a graph problem

Puzzle modeling

Compare two optimization problems

Solve a multicommodity flow minimum cost optimization problem on a randomly created graph

Multi-objective MIP problem with binary variables

Lexicographic goal programming using the Xpress multi-objective API

Multi-objective quadratic optimization

LP solving, modeling variables and constraints, printing the solution

LP solving, modeling variables and constraints

simple LP problem, formulation of blending constraints

MIP solving, binary variables, index set types, logic constraints

LP problem, formulation of resource constraints and material balance constraints, formatted solution printing

QCQP problem

Formulation of resource use profiles

Solve a MIP problem

Solve a nonlinear problem

Modeling a polynomial optimization problem

Modeling with user functions

Multiple problem runs, comparison, blog

MIP, NLP, problem formulations, notebook examples, Xpress Python interface, interactive solving, visualization

xprs_loadproblemdata, displaying a solution as a data frame, a simple pipe workflow

xprs_loadproblemdata, writeprob, setoutput, xprs_optimize, getsolution

xprs_loadproblemdata, getintattrib, getdblattrib, readprob, getmipsol, getsolution

readprob, setintcontrol, writeprob

readprob, setintcontrol, setdefaultcontrol, getintattrib, getdblattrib, setdefaults, dumpcontrols

createprob, readprob, printing, getintattrib

createprob, readprob, mipoptimize, getsolution, addrows, setindicator

readprob, getintattrib, addcboptnode, addcbintnode, getdblattrib

xprs_loadproblemdata, writeprob, xprs_optimize

xprs_loadproblemdata, addrows, getmipsol, mipoptimize

createprob, setprobname, chgbounds, xprs_newcol, xprs_addrow, xprs_newrow, setoutput, getmipsol, mipoptimize

xprs_loadproblemdata, addrows, addcuts, addcboptnode, addcbpreintsol, getcallbacksolution, loaddelayedrows

createprob, chgobjsense, setprobname, xprs_newcol, chgobj, xprs_addrow, getsolution

addmipsol, createprob, xprs_newcol, xprs_newrow, getsolution

createprob, chgobjsense, xprs_newcol, xprs_addrow, getsolution

createprob, chgbounds, xprs_newcol, xprs_newrow, getsolution

createprob, chgbounds, xprs_newcol, xprs_addrow, getsolution

createprob, chgcoltype, chgglblimit, chgrhs, chgobjsense, xprs_newcol, xprs_newrow, getsolution

createprob, setprobname, xprs_newcol, xprs_newrow, xprs_addrow, setoutput, getdblattrib, getsolution

createprob, chgobjsense, chgobj, setprobname, xprs_newcol, xprs_addrow, setoutput, getsolution

createprob, chgbounds, chgobj, setprobname, xprs_newcol, xprs_newrow, setoutput, getsolution

createprob, chgobjsense, setprobname, xprs_newcol, xprs_addrow, setoutput, getsolution

createprob, setprobname, xprs_newcol, xprs_addrow, setoutput, getsolution

createprob, setprobname, addsets, getdblattrib, xprs_newcol, xprs_addrow, setoutput, getsolution

createprob, getiisdata, getintattrib, iisall, iisstatus, iisisolations, xprs_newcol, xprs_newrow, xprs_optimize

bndsa, createprob, getbasis, getnamelist, loadbasis, objsa, rhssa, writebasis, writeslxsol, getsolution, xprs_newcol, xprs_newrow, xprs_optimize

createprob, setoutput, readprob, setintcontrol, tune, tunerreadmethod, tunerwritemethod, xprs_optimize

createprob, setoutput, xprs_newcol, xprs_addrow, chgobj, chgobjn, setobjintcontrol, setobjdblcontrol, xprs_optimize, getintattrib, getmipsol

Mosel subroutine implementing a constraint relation

Constraint definition via value tuples, optimization

Constraint definition, check for feasible solution

Constraint definition

Constraint definition, check for feasible solution, cardinality constraint

Constraint definition

Constraint definition

Constraint definition

Constraint definition, solution callback, branching strategy

Scheduling with resource constraints

Configuring resource and task objects, scheduling solver

Alternative resources, non-constant resource usage profiles

Constraint definition, constraint posting, cpvarlist

Automated propagation, automated post, explicit post, scalar product, dot product

Branching strategy for cpfloatvar

Branching schemes, enumeration for discrete or continuous variables, tasks, disjunctive constraints

Definition of branching callbacks

Setting and retrieving reversible values, behaviour on backtracking

LP or MIP solving within a CP problem

Automated and explicit constraint posting

Data input from file, solving, branching strategy

Linear, 'ocurrence', and 'element' constraints

Linear, 'element', 'disjunctive' constraints

Linear, 'element', 'implies', and 'all-different', 'element' ,'cycle' constraints

'all-different', generic binary, 'cycle' constraints

'abs', 'distance', and 'all-different' constraints; branching strategy, solution callback

Linear, 'element', 'occurrence', 'equiv' constraints; search strategy

Default bounds, cpfloatvar

'all_different', 'implies', 'occurrence', and 'distribute' constraints

'all-different' constraints, propagation algorithm, infeasibility conflict analysis

Linear, 'all-different', and 'element' constraints, solution heuristic

Branching strategy, reversible numbers, branching callbacks

'implies', 'distribute', 'maximum' constraints, symmetry breaking

Scheduling with precedence constraints, task objects

Cumulative scheduling, task and resource objects

Task and resource objects, user search strategy

Provision/requirement of resource, production/consumption of resource

Resource idle times, 'resusage', alternative resources

alldifferent' constraint reformulated by linear relaxations, user-defined linear relaxations

Scheduling objects, branching strategy

Scheduling objects, solution callback

Submodel execution, solution heuristic

Scheduling objects, resource consumption, task modes, RCPSP, MRCPSP, renewable resource, element constraint

Calling Mosel from MATLAB, data exchange in memory

Exchange model parameters and solution between MATLAB and Mosel

Using MATLAB functions in Mosel

Compile/load/run models from MATLAB

Mosel Insight app

lightweight execution, partial entity population, custom execution modes, insightpopulate, insightcapture

test mode, unit testing, pytest

lightweight execution, partial entity population, custom execution modes